on the stability of the reduced basis method for stokes equations in parametrized domains we present an application of reduced basis method for stokes equations in domains with affine parametric dependence the essential components of the method are i the rapid convergence of global reduced basis approximations galerkin projection onto a space wn spanned by solutions of the governing partial differential equation at n selected points in parameter space ii the off line on line computational procedures decoupling the generation and projection stages of the approximation process the operation count for the on line stage in which given a new parameter value we calculate an output of interest depends only on n typically very small and the parametric complexity of the problem the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation design optimization and real time control particular attention is given i to the pressure treatment of incompressible stokes problem ii to find an equivalent inf sup condition that guarantees stability of reduced basis solutions by enriching the reduced basis velocity approximation space with the solutions of a supremizer problem iii to provide algebraic stability of the problem by reducing the condition number of reduced basis matrices using an orthonormalization procedure applied to basis functions iv to reduce computational costs in order to allow real time solution of parametrized problem

exponential time integration for fast finite element solutions of some financial engineering problems we consider exponential time integration schemes for fast numerical pricing of european american barrier and butterfly options when the stock price follows a dynamics described by a jump diffusion process the resulting pricing equation which is in the form of a partial integro differential equation is approximated in space using finite elements our methods require the computation of a single matrix exponential and we demonstrate using a wide range of numerical tests that the combination of exponential integrators and finite element discretisations with quadratic basis functions leads to highly accurate algorithms for cases when the jump magnitude is gaussian comparison with other time stepping methods are also carried out to illustrate the effectiveness of our methods

second order linear differential equations with analytic uncertainties stochastic analysis via the computation of the probability density function abstract this paper concerns the analysis of random second order linear differential equations usually solving these equations consists of computing the first statistics of the response process and that task has been an essential goal in the literature a more ambitious objective is the computation of the solution probability density function we present advances on these two aspects in the case of general random non autonomous second order linear differential equations with analytic data processes the frobenius method is employed to obtain the stochastic solution in the form of a mean square convergent power series we demonstrate that the convergence requires the boundedness of the random input coefficients further the mean square error of the frobenius method is proved to decrease exponentially with the number of terms in the series although not uniformly in time regarding the probability density function of the solution at a given time which is the focus of the paper we rely on the law of total probability to express it in closed form as an expectation for the computation of this expectation a sequence of approximating density functions is constructed by reducing the dimensionality of the problem using the truncated power series of the fundamental set we prove several theoretical results regarding the pointwise convergence of the sequence of density functions and the convergence in total variation the pointwise convergence turns out to be exponential under a lipschitz hypothesis as the density functions are expressed in terms of expectations we propose a crude monte carlo sampling algorithm for their estimation this algorithm is implemented and applied on several numerical examples designed to illustrate the theoretical findings of the paper after that the efficiency of the algorithm is improved by employing the control variates method numerical examples corroborate the variance reduction of the monte carlo approach

fast fourier transform option pricing with stochastic interest rate stochastic volatility and double jumps in this paper we focus on pricing european options in a double exponential jump diffusion model with stochastic volatility and stochastic interest rate firstly using fast fourier transform fft technique we obtain numerical solutions for option prices then we analyze several effects on option prices under the proposed model including correlation between stock returns and volatility stochastic interest rate simulations show that fft is fast and efficient stock returns are negatively correlated with volatility and the effect of stochastic interest rate over longer time horizons is significant

solution of the stochastic radiative transfer equation with rayleigh scattering using rvt technique abstract this paper considers the solution of the radiative transfer equation in a semi infinite continuous stochastic medium with rayleigh scattering the available solutions in literature for this stochastic integro differential equation side are represented only by the ensemble averaged solutions here the deterministic solution of the problem is obtained at first then the random variable transformation rvt technique together with an integral transformation to the input stochastic process is implemented to get the complete stochastic solution of the problem this solution is represented by the probability density function of the solution process moreover the nth statistical moment of the solution is derived numerical results are given for exponential and gaussian distributions of the input stochastic process also these results are given for different boundary conditions

hybrid laplace transform and finite difference methods for pricing american options under complex models abstract in this paper we propose a hybrid laplace transform and finite difference method to price finite maturity american options which is applicable to a wide variety of asset price models including the constant elasticity of variance cev hyper exponential jump diffusion hejd markov regime switching models and the finite moment log stable fmls models we first apply laplace transforms to free boundary partial differential equations pdes or fractional partial differential equations fpdes governing the american option prices with respect to time and obtain second order ordinary differential equations odes or fractional differential equations fdes with free boundary which is named as the early exercise boundary in the american option pricing then we develop an iterative algorithm based on finite difference methods to solve the odes or fdes together with the unknown free boundary values in the laplace space both the early exercise boundary and the prices of american options are recovered through inverse laplace transforms numerical examples demonstrate the accuracy and efficiency of the method in cev hejd markov regime switching models and the fmls models

option pricing with application of levy processes and the minimal variance equivalent martingale measure under uncertainty this paper is dedicated to european option pricing under assumption that the underlying asset follows a geometric levy process the log price of a primary financial instrument has the form of a sum of a drift component a brownian component and a linear combination of time homogeneous poisson processes modeling jumps in price in our approach we apply stochastic analysis especially the change of probability measure techniques as well as fuzzy sets theory to obtain the option valuation formulas we use the minimal variance equivalent martingale measure which requires an advanced analysis of transformation of levy characteristic triplets we obtain analytical option valuation expressions in crisp case moreover we assume that some model parameters are described in an imprecise way and therefore we use their fuzzy counterparts applying fuzzy arithmetic we take into account various types of uncertainty on the market as a result we obtain the analytical option pricing formulas with fuzzy parameters we also propose a method of automatized decision making which utilizes the fuzzy valuation formulas apart from the general pricing expressions we provide numerical examples to illustrate our theoretical results

a developed solution of the stochastic milne problem using probabilistic transformations abstract this paper considers the solution of the milne problem of radiative transfer with isotropic scattering in a continuous stochastic medium properties of the medium are assumed to be continuous random functions of the spatial dimensions the available solutions in literature for this stochastic integro differential equation side are represented only by the ensemble average of the radiant energy density in this paper a developed algorithm based on the implementation of the random variable transformation technique together with an integral transformation to the stochastic properties is introduced a complete stochastic solution represented by the probability density function p d f of the radiant energy density is obtained using the closed form of the p d f the nth moment of the stochastic solution is evaluated in realization of this work exponential and gaussian statistics for the medium properties are assumed results are physically acceptable and found to be compatible with those in the literature

solving second order linear differential equations with random analytic coefficients about ordinary points a full probabilistic solution by the first probability density function abstract this paper deals with the approximate computation of the first probability density function of the solution stochastic process to second order linear differential equations with random analytic coefficients about ordinary points under very general hypotheses our approach is based on considering approximations of the solution stochastic process via truncated power series solution obtained from the random regular power series method together with the so called random variable transformation technique the validity of the proposed method is shown through several illustrative examples

option pricing under a double exponential jump diffusion model this paper aims to extend the analytical tractability of the black scholes model to alternative models with arbitrary jump size distributions more precisely we propose a jump diffusion model for asset prices whose jump sizes have a mixed exponential distribution which is a weighted average of exponential distributions but with possibly negative weights the new model extends existing models such as hyperexponential and double exponential jump diffusion models because the mixed exponential distribution can approximate any distribution as closely as possible including the normal distribution and various heavy tailed distributions the mixed exponential jump diffusion model can lead to analytical solutions for laplace transforms of prices and sensitivity parameters for path dependent options such as lookback and barrier options the laplace transforms can be inverted via the euler inversion algorithm numerical experiments indicate that the formulae are easy to implement and accurate the analytical solutions are made possible mainly because we solve a high order integro differential equation explicitly a calibration example for spy options shows that the model can provide a reasonable fit even for options with very short maturity such as one day this paper was accepted by michael fu stochastic models and simulation

reduced order model for the bgk equation based on pod and optimal transport we present a reduced order approximation of the bgk equation leading to fast and accurate computations the bgk model describes the dynamics of a gas flow in both hydrodynamic and rarefied regimes the particles of the gas are represented by a density distribution function depending on physical space velocity space and time in this work the density distribution function is approximated in the velocity space by a small number of basis functions computed offline in the offline phase the bgk equation is sampled in order to collect information on the density distribution function to complete this sampling optimal transport is used to add new information by interpolating the samples of the density distribution function finally the basis functions are built by proper orthogonal decomposition during the online phase the offline knowledge is used to compute approximations of the density distribution function at low cost to do so the bgk equation is projected onto the basis functions leading to a system of partial differential equations the system obtained is hyperbolic by construction and is solved by an imex runge kutta scheme in time and a finite volume scheme in space to improve the accuracy the reduced oder model is modified to conserve mass momentum and energy of the gas numerical illustrations of 1d and 2d flows are given in particular we investigate the reconstruction and the prediction of shock waves boundary layers and vortices the results demonstrate the accuracy of the reduced order model and the significant reduction of the computational cost

continuous interior penalty finite element method for oseen s equations in this paper we present an extension of the continuous interior penalty method of douglas and dupont interior penalty procedures for elliptic and parabolic galerkin methods in computing methods in applied sciences lecture notes in phys 58 springer verlag berlin 1976 pp 207 216 to oseen s equations the method consists of a stabilized galerkin formulation using equal order interpolation for pressure and velocity to counter instabilities due to the pressure velocity coupling or due to a high local reynolds number we add a stabilization term giving l2 control of the jump of the gradient over element faces edges in two dimensions to the standard galerkin formulation boundary conditions are imposed in a weak sense using a consistent penalty formulation due to nitsche we prove energy type a priori error estimates independent of the local reynolds number and give some numerical examples recovering the theoretical results

immersed boundary smooth extension ibse a high order method for solving incompressible flows in arbitrary smooth domains abstract the immersed boundary method is a simple efficient and robust numerical scheme for solving pde in general domains yet for fluid problems it only achieves first order spatial accuracy near embedded boundaries for the velocity field and fails to converge pointwise for elements of the stress tensor in a previous work we introduced the immersed boundary smooth extension ibse method a variation of the ib method that achieves high order accuracy for elliptic pde by smoothly extending the unknown solution of the pde from a given smooth domain to a larger computational domain enabling the use of simple cartesian grid discretizations in this work we extend the ibse method to allow for the imposition of a divergence constraint and demonstrate high order convergence for the stokes and incompressible navier stokes equations up to third order pointwise convergence for the velocity field and second order pointwise convergence for all elements of the stress tensor the method is flexible to the underlying discretization we demonstrate solutions produced using both a fourier spectral discretization and a standard second order finite difference discretization

proper general decomposition pgd for the resolution of navier stokes equations in this work the pgd method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions in the first stage the equations of stokes and burgers will be solved then we will solve the navier stokes problem in the case of the lid driven cavity for different reynolds numbers re 100 1000 and 10 000 finally the pgd method will be compared to the standard resolution technique both in terms of cpu time and accuracy

continuous interior penalty finite element method for the time dependent navier stokes equations space discretization and convergence this paper focuses on the numerical analysis of a finite element method with stabilization for the unsteady incompressible navier stokes equations incompressibility and convective effects are both stabilized adding an interior penalty term giving l 2 control of the jump of the gradient of the approximate solution over the internal faces using continuous equal order finite elements for both velocities and pressures in a space semi discretized formulation we prove convergence of the approximate solution the error estimates hold irrespective of the reynolds number and hence also for the incompressible euler equations provided the exact solution is smooth

reduced basis approximation and a posteriori error estimation for stokes flows in parametrized geometries roles of the inf sup stability constants in this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady stokes flows in affinely parametrized geometries focusing on the role played by the brezzi s and babuska s stability constants the crucial ingredients of the methodology are a galerkin projection onto a low dimensional space of basis functions properly selected an affine parametric dependence enabling to perform competitive offline online splitting in the computational procedure and a rigorous a posteriori error estimation on field variables the combinatiofn of these three factors yields substantial computational savings which are at the basis of an efficient model order reduction ideally suited for real time simulation and many query contexts e g optimization control or parameter identification in particular in this work we focus on i the stability of the reduced basis approximation based on the brezzi s saddle point theory and the introduction of a supremizer operator on the pressure terms ii a rigorous a posteriori error estimation procedure for velocity and pressure fields based on the babuska s inf sup constant including residuals calculations iii the computation of a lower bound of the stability constant and iv different options for the reduced basis spaces construction we present some illustrative results for both interior and external steady stokes flows in parametrized geometries representing two parametrized classical poiseuille and couette flows a channel contraction and a simple flow control problem around a curved obstacle

the shifted proper orthogonal decomposition a mode decomposition for multiple transport phenomena transport dominated phenomena provide a challenge for common mode based model reduction approaches we present a model reduction method which is suited for these kinds of systems it extends the proper orthogonal decomposition pod by introducing time dependent shifts of the snapshot matrix the approach called shifted proper orthogonal decomposition spod features a determination of the multiple transport velocities and a separation of these one and two dimensional test examples reveal the good performance of the spod for transport dominated phenomena and its superiority in comparison to the pod

american fractional lookback options valuation and premium decomposition this paper deals with valuation and premium decomposition of american fractional lookback options written on dividend paying assets for which exact formulas are unknown except for the perpetual case via a pde approach we derive laplace transforms of the values of lookback call and put options which can be decomposed into the associated european values plus the early exercise premiums using abelian theorems of laplace transforms we characterize asymptotic behaviors of the early exercise boundaries at a time to close to expiration and at infinite time to expiration based on the gaver stehfest inversion method combined with the newton method we develop a fast and accurate algorithm for computing both the option value and the early exercise boundary numerical analysis reveals some notable features of the american fractional lookback options

exit problems for jump processes with applications to dividend problems this paper investigates the first passage times to flat boundaries for hyper exponential jump diffusion processes explicit solutions of the laplace transforms of the distribution of the first passage times the joint distribution of the first passage times and undershoot overshoot the joint distribution of the process and running suprema infima are obtained the processes recover many models appearing in the literature such as the compound poisson risk models the diffusion perturbed compound poisson risk models and their dual models as applications we present explicit expressions of the dividend formulae for barrier strategy and threshold strategy

interior penalty variational multiscale method for the incompressible navier stokes equation monitoring artificial dissipation in this paper we apply the interior penalty method analyzed in e burman and m a fernndez numer math 107 2007 no 1 39 77 mr2317827 2008c 65317 to flows at high reynolds number as a possible measure of solution quality we propose to monitor the ratio between the artificial dissipation induced by the numerical method and the computed physical dissipation for smooth flows we prove that for our method the artificial dissipation serves as an a posteriori error estimator and also that it vanishes at an optimal rate in the case of flows with multiscale features we discuss a heuristic approach relating the decay of the artificial dissipation to the decay rate of the power spectrum some numerical results in two space dimensions are presented examining the relation between the numerical dissipation and solution quality

application of levy processes and esscher transformed martingale measures for option pricing in fuzzy framework in this paper we consider the european option valuation problem we assume that the underlying asset follows a geometric levy process the log price is a sum of a brownian motion with drift and a linear combination of poisson processes describing jumps in price in our approach we use martingale method and theory of fuzzy sets to obtain the european call and put option pricing formulas we use the mean correcting and the esscher transformed martingale measures application of the first mentioned measure required deep analysis of transformation of characteristics of levy process we assume that some model parameters cannot be precisely described and therefore we apply fuzzy numbers application of fuzzy arithmetic enables us to consider different sources of uncertainty and introduce experts opinions or imprecise estimates to the model in contradistinction to our previous papers where the european call option price at time zero was analysed we introduce the valuation expressions of the european call and put options for arbitrary time t numerical simulations conducted in the paper are used to analyse and illustrate the theoretical results this numerical approach is based on l r numbers and the exact shape of the fuzzy numbers which give us the possibility of comparing behaviour of option prices for various values of the parameters of the underlying asset

pricing options under simultaneous stochastic volatility and jumps a simple closed form formula without numerical computational methods abstract we overcome the limitations of the previous literature in the european options pricing in doing so we provide a closed form formula that does not require any numerical computational methods the formula is as simple as the classical black scholes pricing formula in addition we simultaneously include jumps and stochastic volatility our approach implies the introduction of a new class of stochastic processes that are based on clifford algebras the approach can be easily generalized to higher dimensional problems

exact sampling of jump diffusions this paper develops a method for the exact simulation of a skeleton a hitting time and other functionals of a one dimensional jump diffusion with state dependent drift volatility jump intensity and jump size the method requires the drift function to be c1 the volatility function to be c2 and the jump intensity function to be locally bounded no further structure is imposed on these functions the method leads to unbiased simulation estimators of security prices transition densities hitting probabilities and other quantities numerical results illustrate its features

benchmarking the immersed finite element method for fluid structure interaction problems we present an implementation of a fully variational formulation of an immersed method for fluid structure interaction problems based on the finite element method while typical implementation of immersed methods are characterized by the use of approximate dirac delta distributions fully variational formulations of the method do not require the use of said distributions in our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid we assume that the immersed solid can be either viscoelastic of differential type or hyperelastic here we focus on the validation of the method via various benchmarks for fluid structure interaction numerical schemes this is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks

the shifted boundary method for embedded domain computations part i poisson and stokes problems abstract we propose a new finite element method for embedded domain computations which falls in the category of surrogate approximate boundary algorithms the key feature of the proposed approach is the idea of shifting the location where boundary conditions are applied from the true to the surrogate boundary and to appropriately modify the shifted boundary conditions enforced weakly in order to preserve optimal convergence rates of the numerical solution this process yields a method which in our view is simple efficient and also robust since it is not affected by the small cut cell problem although general in nature here we apply this new concept to the poisson and stokes problems we present in particular the full analysis of stability and convergence for the case of the poisson operator and numerical tests for both the poisson and stokes equations for geometries of progressively higher complexity

numerical analysis of american option pricing in a jump diffusion model we discuss pricing formulae for american options in merton s jump diffusion model with the help of variational inequalities we derive some regularity properties of price functions using the finite difference method a discretization scheme is presented and a convergence theorem for the first order derivatives is proved numerical methods and results are also discussed

a new face oriented stabilized xfem approach for 2d and 3d incompressible navier stokes equations abstract we develop a new stabilized xfem based fixed grid approach for the transient incompressible navier stokes equations using cut elements our framework is based on a new flexible strategy to handle several degrees of freedom dofs at nodes required for complex shaped embedded meshes as they occur for fixed grid fluid structure interaction problems boundary conditions on embedded boundaries are imposed weakly using a nitsche type approach ghost penalty terms for velocity and pressure are added for stability reasons and to improve the conditioning of the system matrix the idea of ghost penalties previously developed for stokes problems is extended to the incompressible navier stokes equations by using face oriented fluid stabilizations for both viscous and convective dominated flows furthermore the need for additional terms to enforce boundary conditions for non viscous flows is addressed a detailed numerical study of our stabilized fluid formulation including studies of nitsche s parameter and the ghost penalty parameter shows optimal error convergence and a good system conditioning in the viscous and the convective dominated cases compared to other fixed grid fluid formulations our method is much more accurate and less sensitive to the location of the interface regarding the accuracy and the sensitivity with respect to the interface position a clear improvement could be observed for the viscous and pressure fluxes as well as for the imposition of the boundary condition results of a transient two dimensional high reynolds number flow over a cylinder and the flow over a thick plate in 3d confirm the applicability of the proposed method

tensor transform based quaternion fourier transform algorithm we present a concept of the tensor representation of color images in quaternion algebra we present concepts of direction components composing the color image we propose a new method of the 2 d quaternion discrete fourier transform qdft we calculate the 2 d qdft with minimum number of operations of multiplication we examine the proposed method in rgb color image model the traditional fourier transform is a fundamental tool in signal and image processing which in color imaging transforms images either in monochrome or as separate color channels thereby ignoring interactions between the color channels the quaternion discrete fourier transform qdft a generalization of the fourier transform represents the three color channels of an image in the rgb color space as a vector field in the quaternion arithmetic allowing for simultaneous analysis of all color data it is expected that this new color imaging model which captures the interactions between the different color channels will improve upon existing image processing and recognition systems efficient qdft algorithms are derived by combining classical dft transforms enabling standard fast fourier transform fft software to provide a fast qdft numerical implementation we developed an open source quaternion fourier transform tool that calculates the 2 d qdft by the column row method which is performed by calculating multiple 1 d qdfts where each 1 d transform is calculated by two complex 1 d dfts the matrices involved in these calculations necessitate the inclusion of a discussion on symplectic decomposition our main contribution is the presentation a new algorithm for the tensor representation of the qdft that is structurally simpler and uses less multiplications than its predecessors for instance for the images of size n i n where n 2 r r 2 the tensor 2 d qdft saves about 2 n 2 r real multiplications

time varying jump tails we develop new methods for the estimation of time varying risk neutral jump tails in asset returns in contrast to existing procedures based on tightly parameterized models our approach imposes much fewer structural assumptions relying on extreme value theory approximations together with short maturity options the new estimation approach explicitly allows the parameters characterizing the shape of the right and the left tails to differ and importantly for the tail shape parameters to change over time on implementing the procedures with a panel of s p 500 options our estimates clearly suggest the existence of highly statistically significant temporal variation in both of the tails we further relate this temporal variation in the shape and the magnitude of the jump tails to the underlying return variation through the formulation of simple time series models for the tail parameters

cutfem discretizing geometry and partial differential equations we discuss recent advances on robust unfitted finite element methods on cut meshes these methods are designed to facilitate computations on complex geometries obtained for example from computer

hp adaptive ipdg tdg fem for parabolic obstacle problems for a parabolic obstacle problem two equivalent hp fem discretization methods based on interior penalty discontinuous galerkin in space and discontinuous galerkin in time are presented the first approach is based on a variational inequality vi formulation and the second approach on a mixed method in which the non penetration condition is resolved by a lagrange multiplier the discrete lagrange multiplier is a linear combination of biorthogonal basis functions allowing to write the discrete vi constraints as a set of complementarity problems employing a penalized fischer burmeister non linear complementarity function the discrete mixed problem can be solved by a locally q quadratic converging semi smooth newton ssn method the hierarchical a posteriori error estimator for the vi formulation which under the saturation assumption is both efficient and reliable allows hp adaptivity the numerical experiments show improved convergence compared to uniform and h adaptive meshes furthermore an a priori error estimate is given for the vi formulation

option pricing and hedging in incomplete market driven by normal tempered stable process with stochastic volatility abstract this paper develops a distribution class termed normal tempered stable by subordinating a drifted brownian motion through a strictly increasing tempered stable process that generalizes the variance gamma and the normal inverse gaussian and is used to model the logarithm asset returns the newly added parameter is to create subclasses for all the distributions discovered in financial market the empirical test suggests that time series of technology stock returns in us market reject both the variance gamma distribution and the normal inverse gaussian distribution and admit instead another subclass of the normal tempered stable distribution furthermore we introduce stochastic volatilities into the normal tempered stable process and derive explicit formulae for option pricing and hedging by means of the characteristic function based methods to answer the question of how well different models work in practice we investigate four models adopting data on daily equity option prices and obtain several findings from the numerical results to sum up the normal tempered stable process with stochastic volatility is able to adequately capture implied volatility dynamics and seen as a superior model relative to the jump diffusion stochastic volatility model based on the construction methodology that incorporates more sophisticated and flexible jump structure and the systematic and realistic treatment of volatility dynamics the normal tempered stable model turns out to have the competitive performance in an efficient manner given that it only requires three parameters

iterative algorithm for the first passage time distribution in a jump diffusion model with regime switching and its applications for a regime switching model with a finite number of regimes and double phase type jumps jiang and pistorius 2008 derived matrix equations with real parameters for the wiener hopf factorization the laplace transform of the first passage time distribution is expressed in terms of the solution of the matrix equations in this paper we provide an iterative algorithm for solving the matrix equations of jiang and pistorius 2008 with complex parameters this makes it possible to obtain numeric values of the laplace transform with complex parameters for the first passage time distribution the laplace transform with complex parameters can be inverted by numerical inversion algorithms such as the euler method as an application we compute the prices of defaultable bonds under a structural model with regime switching and double phase type jumps

advection modes by optimal mass transfer classical model reduction techniques approximate the solution of a physical model by a limited number of global modes these modes are usually determined by variants of principal component analysis global modes can lead to reduced models that perform well in terms of stability and accuracy however when the physics of the model is mainly characterized by advection the non local representation of the solution by global modes essentially reduces to a fourier expansion in this paper we describe a method to determine a low order representation of advection this method is based on the solution of monge kantorovich mass transfer problems examples of application to point vortex scattering korteweg de vries equation von k arm an wake and hurricane dean advection are discussed

generalized ait sahalia type interest rate model with poisson jumps and convergence of the numerical approximation abstract in this paper we consider a generalized ait sahalia interest rate model with poisson jumps in finance the analytical properties including positivity boundedness and pathwise asymptotic estimations of the solution to this model are investigated moreover we prove that the euler maruyama em numerical solution converges to the true solution of the model in probability finally we apply the em solution to compute some financial quantities a numerical example is provided to demonstrate the effectiveness of our results

projection based reduced order models for a cut finite element method in parametrized domains abstract this work presents a reduced order modeling technique built on a high fidelity embedded mesh finite element method such methods and in particular the cutfem method are attractive in the generation of projection based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains and in general to handle topological changes the combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems avoiding remeshing as well as the reference domain formulation often used in the reduced order modeling for boundary fitted finite element formulations the resulting novel methodology is presented on linear elliptic and stokes problems together with several test cases to assess its capability the role of a proper extension and transport of embedded solutions to a common background is analyzed in detail

option pricing using the fast fourier transform under the double exponential jump model with stochastic volatility and stochastic intensity this paper is based on the fft fast fourier transform approach for the valuation of options when the underlying asset follows the double exponential jump process with stochastic volatility and stochastic intensity our model captures three terms structure of stock prices the market implied volatility smile and jump behavior via the fft method numerical examples using european call options show effectiveness of the proposed model meanwhile numerical results prove that the fft approach is considerably correct fast and competent

perpetual american options under levy processes we consider perpetual american options assuming that under a chosen equivalent martingale measure the stock returns follow a levy process for put and call options their analogues for more general payoffs and a wide class of levy processes that contains brownian motion normal inverse gaussian processes hyperbolic processes truncated levy processes and their mixtures we obtain formulas for the optimal exercise price and the fair price of the option in terms of the factors in the wiener hopf factorization formula i e in terms of the resolvents of the supremum and infimum processes and derive explicit formulas for these factors for calls puts and some other options the results are valid for any levy process we use dynkin s formula and the wiener hopf factorization to find the explicit formula for the price of the option for any candidate for the exercise boundary and by using this explicit representation we select the optimal solution we show that in some cases the principle of the smooth fit fails and suggest a generalization of this principle

optimal stopping of markov processes hilbert space theory approximation algorithms and an application to pricing high dimensional financial derivatives the authors develop a theory characterizing optimal stopping times for discrete time ergodic markov processes with discounted rewards the theory differs from prior work by its view of per stage and terminal reward functions as elements of a certain hilbert space in addition to a streamlined analysis establishing existence and uniqueness of a solution to bellman s equation this approach provides an elegant framework for the study of approximate solutions in particular the authors propose a stochastic approximation algorithm that tunes weights of a linear combination of basis functions in order to approximate a value function they prove that this algorithm converges almost surely and that the limit of convergence has some desirable properties the utility of the approximation method is illustrated via a computational case study involving the pricing of a path dependent financial derivative security that gives rise to an optimal stopping problem with a 100 dimensional state space

reduction of nonlinear embedded boundary models for problems with evolving interfaces embedded boundary methods alleviate many computational challenges including those associated with meshing complex geometries and solving problems with evolving domains and interfaces developing model reduction methods for computational frameworks based on such methods seems however to be challenging indeed most popular model reduction techniques are projection based and rely on basis functions obtained from the compression of simulation snapshots in a traditional interface fitted computational framework the computation of such basis functions is straightforward primarily because the computational domain does not contain in this case a fictitious region this is not the case however for an embedded computational framework because the computational domain typically contains in this case both real and ghost regions whose definitions complicate the collection and compression of simulation snapshots the problem is exacerbated when the interface separating both regions evolves in time this paper addresses this issue by formulating the snapshot compression problem as a weighted low rank approximation problem where the binary weighting identifies the evolving component of the individual simulation snapshots the proposed approach is application independent and therefore comprehensive it is successfully demonstrated for the model reduction of several two dimensional vortex dominated fluid structure interaction problems

cut finite element methods for elliptic problems on multipatch parametric surfaces we develop a finite element method for the laplace beltrami operator on a surface described by a set of patchwise parametrizations the patches provide a partition of the surface and each patch is

galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics error estimates for galerkin proper orthogonal decomposition pod methods for nonlinear parabolic systems arising in fluid dynamics are proved for the time integration the backward euler scheme is considered the asymptotic estimates involve the singular values of the pod snapshot set and the grid structure of the time discretization as well as the snapshot locations

random hermite differential equations mean square power series solutions and statistical properties abstract this paper deals with the construction of random power series solution of second order linear differential equations of hermite containing uncertainty through its coefficients and initial conditions under appropriate hypotheses on the data we establish that the constructed random power series solution is mean square convergent we provide conditions in order to obtain random polynomial solutions and as a consequence random hermite polynomial are introduced also the main statistical functions of the approximate stochastic process solution generated by truncation of the exact power series solution are given finally we apply the proposed technique to several illustrative examples comparing the numerical results with respect to those provided by other available approaches including monte carlo simulation

random differential operational calculus theory and applications in this article we obtain a product rule and a chain rule for mean square derivatives an application of the chain rule to the mean square solution of random differential equations is shown however to achieve such mean square differentiation rules fourth order properties were needed and therefore we first studied a mean fourth order differential and integral calculus results are applied to solve random linear variable coefficient differential problems

the probability density function to the random linear transport equation we present a formula to calculate the probability density function of the solution of the random linear transport equation in terms of the density functions of the velocity and the initial condition we also present an expression for the joint probability density function of the solution in two different points our results have shown good agreement with monte carlo simulations

using fem rvt technique for solving a randomly excited ordinary differential equation with a random operator the technique of stochastic finite element sfem which is the finite element technique fem adapted to stochastic problems can be re described to use random variable transformation technique rvt a new fem rvt technique was successfully used in solving stochastic problems with random excitation m el tawil w el tahhan a hussein a proposed technique of sfem on solving ordinary random differential equation j appl math comput 161 2005 35 47 in this paper the technique is adapted to solve a randomly excited differential equation with a random operator the technique shows high accuracy when solving a case study compared with the exact solution finally a problem with unknown exact solution is solved using this technique

stability and accuracy of periodic flow solutions obtained by a pod penalty method we develop a new penalty method to derive low dimensional galerkin models for fluid flows with time dependent boundary conditions we then outline a procedure based on bifurcation analysis in selecting the proper values of the penalty parameter s that yield asymptotically stable periodic solutions of the highest possible accuracy we illustrate this new approach by studying flow past a circular cylinder using direct numerical simulation dns data and a wave structure interaction problem using particle image velocimetry piv data

the shifted boundary method for embedded domain computations part ii linear advection diffusion and incompressible navier stokes equations abstract we propose a new embedded finite element method for the linear advection diffusion equation and the laminar and turbulent incompressible navier stokes equations the proposed method belongs to the class of surrogate approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary accordingly boundary conditions enforced weakly are appropriately modified to preserve optimal error convergence rates we include the full analysis of stability and convergence of the method in the linear advection diffusion equation and a battery of tests for the case of laminar and turbulent incompressible navier stokes equations we also discuss the conservation properties of the proposed method in all cases

pricing turbo warrants under mixed exponential jump diffusion model abstract turbo warrant is a special type of barrier options in which the rebate is calculated as another exotic option in this paper using laplace transforms we obtain the valuation of turbo warrant under the mixed exponential jump diffusion model which is able to approximate any jump size distribution the numerical laplace inversion examples verify that the analytical solutions are accurate the results of simulation confirm the argument that jump risk should not be ignored in the valuation of turbo warrants

a geometric levy model for n fold compound option pricing in a fuzzy framework in this paper we study the problem of n fold compound option valuation using the martingale method and the theory of fuzzy sets we adopt a geometric levy process for modeling the underlying asset price dynamics the log price is the sum of a brownian motion with drift and a poisson process describing jumps in the price to obtain the pricing formula for n fold compound option we use the esscher transformed martingale measure as the equivalent martingale measure the major challenge in deriving the closed form analytic expression for n fold compound options is to calculate complex multivariate normal integrals the complexity is due to the sophisticated structure of the options in order to overcome this difficulty we prove a mathematical expectation related to multivariate normal variables to the best of our knowledge this report describes the first time that such an approach has been adopted and it is highly useful in the pricing of n fold compound options and many other financial derivatives because the uncertainty in financial markets simultaneously involves randomness and fuzziness we assume that the underlying asset price follows a fuzzy stochastic process under this assumption the cut of the fuzzy price of n fold compound call options is derived considering a decision maker s subjective judgment the permissible range of the expected prices of n fold compound call options with uncertainty is given finally numerical examples are presented to illustrate and analyze the theoretical results

pricing dynamic fund protections with regime switching this paper deals with the valuation of dynamic fund protections in a markov regime switching environment the volatility switches over time subject to a continuous time markov chain using a regime switching diffusion process to describe the primary mutual fund value explicit solutions of the laplace transforms of the value of the dynamic fund protection are obtained through martingale technique moreover we analyze the value of dynamic fund protections under a generalized regime switching jump diffusion model due to the complexity of markov regime switching the jump process involved and the nonlinearity closed form formulas for dynamic fund protection prices are virtually impossible to obtain we design a numerical algorithm according to the markov chain approximation techniques and obtain numerical results of the value of dynamic fund protection

a nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity in this note we propose a finite element method for incompressible or compressible elasticity problems with discontinuous modulus of elasticity or if compressible poisson s ratio the problem is written on mixed form using p1 continuous displacements and elementwise p0 pressures leading to the possibility of eliminating the pressure beforehand in the compressible case in the incompressible case the method is augmented by a stabilization term penalizing the pressure jumps we show a priori error estimates under certain regularity hypothesis in particular we prove that if the exact solution is sufficiently smooth in each subdomain then the convergence order is optimal

an extended finite element method lagrange multiplier based approach for fluid structure interaction abstract this paper presents a new fixed grid fluid structure interaction scheme that can be applied to the interaction of most general structures with incompressible flow it is based on an extended finite element method xfem based strategy the extended eulerian fluid field and the lagrangian structural field are partitioned and iteratively coupled using lagrange multiplier techniques for non matching grids the approach allows the simulation of the interaction of thin and bulky structures exhibiting large deformations finally qualitative examples and a benchmark computation demonstrate key features and accuracy of the method

the shifted boundary method for hyperbolic systems embedded domain computations of linear waves and shallow water flows abstract we propose a new computational approach for embedded boundary simulations of hyperbolic systems and in particular the linear wave equations and the nonlinear shallow water equations the proposed approach belongs to the class of surrogate approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary accordingly boundary conditions enforced weakly are appropriately modified to preserve optimal error convergence rates this framework is applied here in the setting of a stabilized finite element method even though other spatial discretization techniques could have been employed accuracy stability and robustness of the proposed method are tested by means of an extensive set of computational experiments for the acoustic wave propagation equations and shallow water equations comparisons with standard weak boundary conditions imposed on body fitted grids which conform to the geometry of the computational domain boundaries are also presented

enablers for robust pod models this paper focuses on improving the stability as well as the approximation properties of reduced order models rom based on proper orthogonal decomposition pod the rom is obtained by seeking a solution belonging to the pod subspace and that at the same time minimizes the navier stokes residuals we propose a modified rom that directly incorporates the pressure term in the model the rom is then stabilized making use of a method based on the fine scale equations an improvement of the pod solution subspace is performed thanks to an hybrid method that couples direct numerical simulations and reduced order model simulations the methods proposed are tested on the two dimensional confined square cylinder wake flow in laminar regime

pricing of options in the singular perturbed stochastic volatility model the pricing of options in the fast mean reverting stochastic volatility model using the singular perturbation method has received a considerable amount of attention in the last two decades however it is not to easy to estimate the accuracy of the approximation if the payoff function is not smooth or bounded as is the case for european call options in this article we introduce a new novel approach for pricing options in the fast mean reverting stochastic volatility model combinations of fourier analysis and singular perturbation methods enable us to estimate the accuracy easily we also show that this method allows us to derive the price of european and bermudan options in the fast mean reverting stochastic volatility environment with jumps

currency option pricing with wishart process it has been well documented that foreign exchange rates exhibit both mean reversion and stochastic volatility in addition to these recent empirical evidence shows a stochastic skew of implied volatility surface from currency option data which means that the slope of implied volatility curve of a given maturity is stochastically time varying this paper develops a currency option pricing model which accommodates for this phenomena the proposed model postulates that the log currency value follows a mean reverting process with stochastic volatility driven by wishart process under risk neutral measure pricing formula for european currency option is derived in terms of fourier transform benchmarking against the monte carlo simulation our numerical examples reveal that the pricing formula is accurate and remarkably efficient the proposed model is also generalized to include jumps the ability of the our model on capturing stochastic skew is illustrated through a numerical example

random airy type differential equations mean square exact and numerical solutions this paper deals with the construction of power series solutions of random airy type differential equations containing uncertainty through the coefficients as well as the initial conditions under appropriate hypotheses on the data we establish that the constructed random power series solution is mean square convergent over the whole real line in addition the main statistical functions such as the mean and the variance of the approximate solution stochastic process generated by truncation of the exact power series solution are given finally we apply the proposed technique to several illustrative examples which show substantial speed up and improvement in accuracy compared to other approaches such as monte carlo simulations

fft based option pricing under a mean reverting process with stochastic volatility and jumps numerous studies present strong empirical evidence that certain financial assets may exhibit mean reversion stochastic volatility or jumps this paper explores the valuation of european options when the underlying asset follows a mean reverting log normal process with stochastic volatility and jumps a closed form representation of the characteristic function of the process is derived for the computation of european option prices via the fast fourier transform

iterative bregman projections for regularized transportation problems this article details a general numerical framework to approximate so lutions to linear programs related to optimal transport the general idea is to introduce an entropic regularization of the initial linear program this regularized problem corresponds to a kullback leibler bregman di vergence projection of a vector representing some initial joint distribu tion on the polytope of constraints we show that for many problems related to optimal transport the set of linear constraints can be split in an intersection of a few simple constraints for which the projections can be computed in closed form this allows us to make use of iterative bregman projections when there are only equality constraints or more generally bregman dykstra iterations when inequality constraints are in volved we illustrate the usefulness of this approach to several variational problems related to optimal transport barycenters for the optimal trans port metric tomographic reconstruction multi marginal optimal trans port and in particular its application to brenier s relaxed solutions of in compressible euler equations partial un balanced optimal transport and optimal transport with capacity constraints

pricing and hedging european style options in levy based stochastic volatility models considering the leverage effect abstract this paper develops a semi analytical exact solution for the discrete time variance optimal hedging strategy based on two dimensional fourier cosine series expansions this approach is novel and is more efficient than those previously suggested in the literature numerical studies for different models also suggest that the algorithm has better accuracy and stability for the pricing and hedging problems a levy based stochastic volatility model considering the leverage effect is also proposed we have employed data on apple stock prices and the corresponding option contracts to test this model to evaluate its ability to perform pricing and hedging in summary our model design is relatively reliable in the context of the known empirical patterns such as the existence of jumps the volatility smile and the negative correlation between asset returns and volatilities

the approximate solutions of some stochastic differential equations using transformations in this paper the transformation technique together with a numerical technique is used to obtain an approximate probability density function pdf for the solution process of some stochastic differential equations the approach is applied on some first order and second order differential equations with making comparisons with the exact solution if possible

a reduced order shifted boundary method for parametrized incompressible navier stokes equations abstract we investigate a projection based reduced order model of the steady incompressible navier stokes equations for moderate reynolds numbers in particular we construct an embedded reduced basis space by applying proper orthogonal decomposition to the shifted boundary method a high fidelity embedded method recently developed we focus on the geometrical parametrization through level set geometries using a fixed cartesian background geometry and the associated mesh this approach avoids both remeshing and the development of a reference domain formulation as typically done in fitted mesh finite element formulations two dimensional computational examples for one and three parameter dimensions are presented to validate the convergence and the efficacy of the proposed approach

on the stability and convergence of a galerkin reduced order model rom of compressible flow with solid wall and far field boundary treatment a reduced order model rom based on the proper orthogonal decomposition pod galerkin projection method is proposed as an alternative discretization of the linearized compressible euler equations it is shown that the numerical stability of the rom is intimately tied to the choice of inner product used to define the galerkin projection for the linearized compressible euler equations a symmetry transformation motivates the construction of a weighted l 2 inner product that guarantees certain stability bounds satisfied by the rom sufficient conditions for well posedness and stability of the present galerkin projection method applied to a general linear hyperbolic initial boundary value problem ibvp are stated and proven well posed and stable far field and solid wall boundary conditions are formulated for the linearized compressible euler rom using these more general results a convergence analysis employing a stable penalty like formulation of the boundary conditions reveals that the rom solution converges to the exact solution with refinement of both the numerical solution used to generate the rom and of the pod basis an a priori error estimate for the computed rom solution is derived and examined using a numerical test case published in 2010 by john wiley sons ltd

exact simulation of stochastic volatility and other affine jump diffusion processes the stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated discretization methods can be used for simulating security prices under these models however discretization introduces bias into the simulation results and a large number of time steps may be needed to reduce the discretization bias to an acceptable level this paper suggests a method for the exact simulation of the stock price and variance under hestons stochastic volatility model and other affine jump diffusion processes the sample stock price and variance from the exact distribution can then be used to generate an unbiased estimator of the price of a derivative security we compare our method with the more conventional euler discretization method and demonstrate the faster convergence rate of the error in our method specifically our method achieves an o s 1 2 convergence rate where s is the total computational budget the convergence rate for the euler discretization method is o s 1 3 or slower depending on the model coefficients and option payoff function

solution of the stochastic transport equation of neutral particles with anisotropic scattering using rvt technique much of the literatures are directed toward the development of a mathematical formalism for a rigorous estimation of the ensemble average of the solution process of a stochastic differential equation sde the random variable transformation technique rvt is a powerful technique to get the complete solution for the sde represented by the probability density function of the solution process in this paper the rvt technique together with a simple integral transformation to the input stochastic process are implemented to get the complete solution of the one speed transport equation for neutral particles in a semi infinite stochastic medium with linear anisotropic scattering the extinction function of the medium input stochastic process is assumed to be a continuous random function of position the probability density function and hence the higher order statistical moments of the solution process are presented numerical results are given for different distributions of the input stochastic process

an unfitted nitsche method for incompressible fluid structure interaction using overlapping meshes we consider the extension of the nitsche method to the case of fluid structure interaction problems on unfitted meshes we give a stability analysis for the space semi discretized problem and show how this estimate may be used to derive optimal error estimates for smooth solutions irrespectively of the mesh interface intersection we also discuss different strategies for the time discretization using either fully implicit or explicit coupling loosely coupled schemes some numerical examples illustrate the theoretical discussion

stabilization of explicit coupling in fluid structure interaction involving fluid incompressibility abstract in this work we propose a stabilized explicit coupling scheme for fluid structure interaction problems involving a viscous incompressible fluid the coupled discrete formulation is based on nitsche s method with a time penalty term giving l 2 control on the fluid pressure variations at the interface for a linear model problem we prove that the scheme is stable in the energy norm irrespectively of the so called added mass effect namely the fluid structure density ratio and the geometry of the domain numerical experiments in the linear and non linear case show that optimal time accuracy can be obtained by performing one defect correction iteration

a fast lattice green s function method for solving viscous incompressible flows on unbounded domains a computationally efficient method for solving three dimensional viscous incompressible flows on unbounded domains is presented the method formally discretizes the incompressible navier stokes equations on an unbounded staggered cartesian grid operations are limited to a finite computational domain through a lattice green s function technique this technique obtains solutions to inhomogeneous difference equations through the discrete convolution of source terms with the fundamental solutions of the discrete operators the differential algebraic equations describing the temporal evolution of the discrete momentum equation and incompressibility constraint are numerically solved by combining an integrating factor technique for the viscous term and a half explicit runge kutta scheme for the convective term a projection method that exploits the mimetic and commutativity properties of the discrete operators is used to efficiently solve the system of equations that arises in each stage of the time integration scheme linear complexity fast computation rates and parallel scalability are achieved using recently developed fast multipole methods for difference equations the accuracy and physical fidelity of solutions are verified through numerical simulations of vortex rings

certified reduced basis methods for parametrized saddle point problems we present reduced basis approximations and associated rigorous a posteriori error bounds for parametrized saddle point problems first we develop new a posteriori error estimates that unlike earlier approaches provide upper bounds for the errors in the approximations of the primal variable and the lagrange multiplier separately the proposed method is an application of brezzi s theory for saddle point problems to the reduced basis context and exhibits significant advantages over existing methods second based on an analysis of brezzi s theory we compare several options for the reduced basis approximation space from the perspective of approximation stability and computational cost finally we introduce a new adaptive sampling procedure for saddle point problems constructing approximation spaces that are stable and compared to earlier approaches computationally much more efficient the method is applied to a stokes flow problem in a two dimensional channel with a parametrized rectangular obstacle

pricing options in jump diffusion models an extrapolation approach we propose a new computational method for the valuation of options in jump diffusion models the option value function for european and barrier options satisfies a partial integrodifferential equation pide this pide is commonly integrated in time by implicit explicit imex time discretization schemes where the differential diffusion term is treated implicitly while the integral jump term is treated explicitly in particular the popular imex euler scheme is first order accurate in time second order accuracy in time can be achieved by using the imex midpoint scheme in contrast to the above approaches we propose a new high order time discretization scheme for the pide based on the extrapolation approach to the solution of odes that also treats the diffusion term implicitly and the jump term explicitly the scheme is simple to implement can be added to any pide solver based on the imex euler scheme and is remarkably fast and accurate we demonstrate our approach on the examples of merton s and kou s jump diffusion models the diffusion extended variance gamma model as well as the two dimensional duffie pan singleton model with correlated and contemporaneous jumps in the stock price and its volatility by way of example pricing a one year double barrier option in kou s jump diffusion model our scheme attains accuracy of 10 5 in 72 time steps in 0 05 seconds in contrast it takes the first order imex euler scheme more than 1 3 million time steps in 873 seconds and the second order imex midpoint scheme 768 time steps in 0 49 seconds to attain the same accuracy our scheme is also well suited for bermudan options combining simplicity of implementation and remarkable gains in computational efficiency we expect this method to be very attractive to financial engineering modelers

a reduced order method for simulation and control of fluid flows this article presents a reduced order modeling approach for simulation and control of viscous incompressible flows the reduced order models suitable for control and which capture the essential physics are developed using the reduced basis method the so called lagrange approach is used to define reduced bases and the basis functions in this approach are obtained from the numerical solutions the feasibility of this method for flow control is demonstrated on boundary control problems in closed cavity and in wall bounded channel flows control action is effected through boundary surface movement on a part of the solid wall our formulation of the reduced order method applied to flow control problems leads to a constrained minimization problem and is solved by applying newton like methods to the necessary conditions of optimality through our computational experiments we demonstrate the feasibility and applicability of the reduced order method for simulation and control of fluid flows

numerical valuation of european and american options under kou s jump diffusion model numerical methods are developed for pricing european and american options under kou s jump diffusion model which assumes the price of the underlying asset to behave like a geometrical brownian motion with a drift and jumps whose size is log double exponentially distributed the price of a european option is given by a partial integro differential equation pide while american options lead to a linear complementarity problem lcp with the same operator spatial differential operators are discretized using finite differences on nonuniform grids and time stepping is performed using the implicit rannacher scheme for the evaluation of the integral term easy to implement recursion formulas are derived which have optimal computational cost when pricing european options the resulting dense linear systems are solved using a stationary iteration for american options two ways to solve the lcps are described an operator slitting method and a penalty method numerical experiments confirm that the developed methods are very efficient as fairly accurate option prices can be computed in a few milliseconds on a pc

default probability of american lookback option in a mixed jump diffusion model abstract this paper considers the default probability of american lookback option in a mixed jump diffusion model where the underlying asset price has to cross two sided predetermined strikes to activate the american lookback option we study a default problem with the bankruptcy time being defined as the first passage time of the underlying asset price by solving a system of coupled mjd fbm we obtain an explicit formula for the laplace transform of the default time some numerical results are given for illustration

the immersed boundary method a projection approach a new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion like previous methods a boundary force is applied at the immersed surface to satisfy the no slip constraint this extra constraint can be added to the incompressible navier stokes equations by introducing regularization and interpolation operators the current method gives prominence to the role of the boundary force acting as a lagrange multiplier to satisfy the no slip condition this role is analogous to the effect of pressure on the momentum equation to satisfy the divergence free constraint the current immersed boundary method removes slip and non divergence free components of the velocity field through a projection the boundary force is determined implicitly without any constitutive relations allowing the present formulation to use larger cfl numbers compared to some past methods symmetry and positive definiteness of the system are preserved such that the conjugate gradient method can be used to solve for the flow field examples show that the current formulation achieves second order temporal accuracy and better than first order spatial accuracy in l 2 norms for one and two dimensional test problems results from two dimensional simulations of flows over stationary and moving cylinders are in good agreement with those from previous experimental and numerical studies

supremizer stabilization of pod galerkin approximation of parametrized steady incompressible navier stokes equations in this work we present a stable proper orthogonal decomposition pod galerkin approximation for parametrized steady incompressible navier stokes equations with low reynolds number supremizers solutions are added to the reduced velocity space in order to obtain a stable reduced order system considering in particular the fulfillment of an inf sup condition the stability analysis is first carried out from a theoretical standpoint then confirmed by numerical tests performed on a parametrized two dimensional backward facing step flow

testing for jumps when asset prices are observed with noise a swap variance approach abstract this paper proposes a new test for jumps in asset prices that is motivated by the literature on variance swaps formally the test follows by a direct application of ito s lemma to the semi martingale process of asset prices and derives its power from the impact of jumps on the third and higher order return moments intuitively the test statistic reflects the cumulative gain of a variance swap replication strategy which is known to be minimal in the absence of jumps but substantial in the presence of jumps simulations show that the jump test has nice properties and is generally more powerful than the widely used bi power variation test an important feature of our test is that it can be applied in analytically modified form to noisy high frequency data and still retain power as a by product of our analysis we obtain novel analytical results regarding the impact of noise on bi power variation an empirical illustration using ibm trade data is also included

on pricing barrier options with regime switching we consider the valuation of both european style and american style barrier options in a markovian regime switching black scholes merton economy where the price process of an underlying risky asset is governed by a markovian regime switching geometric brownian motion both the probabilistic and partial differential equation pde approaches are used to price the barrier options for the probabilistic approach to value a european style barrier option we employ the fundamental matrix solution and the fourier transform space to derive a semi analytical solution the pde approach is employed to value an american barrier option where we obtain a system of free boundary coupled pdes and an analytical quadratic approximation to the price by solving the free boundary problem