restricted ornstein uhlenbeck process and applications in neuronal models with periodic input signals restricted gauss markov processes are used to construct inhomogeneous leaky integrate and fire stochastic models for single neurons activity in the presence of a lower reflecting boundary and periodic input signals the first passage time problem through a time dependent threshold is explicitly developed numerical simulation and asymptotic results for firing densities are provided

parameterization and adaptive control of multivariable noncanonical t s fuzzy systems this paper conducts a new study for adaptive takagi sugeno t s fuzzy approximation based control of multi input and multi output mimo noncanonical form nonlinear systems canonical form nonlinear systems have explicit relative degree structures whose approximation models can be directly used to derive desired parameterized controllers noncanonical form nonlinear systems usually do not have such a feature nor do their approximation models which are also in noncanonical forms this paper shows that it is desirable to reparameterize noncanonical form t s fuzzy system models with smooth membership functions for adaptive control and such system reparameterization can be realized using relative degrees a concept yet to be studied for mimo noncanonical form t s fuzzy systems this paper develops an adaptive feedback linearization scheme for control of such general system models with uncertain parameters by first deriving various relative degree structures and normal forms for such systems then a reparameterization procedure is developed for such system models based on which adaptive control designs are derived with desired stability and tracking properties analyzed a detailed example is presented with simulation results to show the new control design procedure and desired control system performance

the perturbed compound poisson risk model with two sided jumps in this paper we consider a perturbed compound poisson risk model with two sided jumps the downward jumps represent the claims following an arbitrary distribution while the upward jumps are also allowed to represent the random gains assuming that the density function of the upward jumps has a rational laplace transform the laplace transforms and defective renewal equations for the discounted penalty functions are derived and the asymptotic estimate for the probability of ruin is also studied for heavy tailed downward jumps finally some explicit expressions for the discounted penalty functions as well as numerical examples are given

characterizations of classes of stable matrices abstract this paper extends some results on the structure of subsets of the set of stable matrices for these subsets different characterizations are obtained using the set product defined in this paper as well as inertia and algebraic characterizations for low dimensions 2 2 and 3 3 matrices some inclusion relations that hold for these classes of matrices are proved and some open questions mentioned

default probabilities of a holding company with complete and partial information abstract this paper studies the valuation of credit risk for firms that own several subsidiaries or business lines we provide simple analytical approximating expressions for probabilities of default and for equity debt market values both in the case when the information is available in continuous time as well as in the case that it is not instantaneously available the total firm s asset value being modeled as a sum of lognormal random variables we use convex upper and lower approximations to infer these analytical approximating expressions we extend the model to firms financed by multiple stochastic liabilities and conclude by numerical illustrations

financial options pricing with regime switching jump diffusions we present a numerical method to evaluate financial derivatives under regime switching jump diffusion models the prices of european and american options are derived by solving a partial integro differential equation pide and a linear complementarity problem lcp respectively we use the implicit method with three time levels to solve the pide and apply it coupled with the operator splitting method to solve the lcp the proposed method has the advantage not only to avoid any fixed point iteration techniques at each time step but also to evaluate directly the prices of the european and american options at all states of the economy it is proved that the implicit method to solve the pide for the european option problem is stable with the second order accuracy in the discrete 2 norm we perform some numerical simulations to illustrate the analysis of the proposed method under the regime switching jump diffusion models

technical communique some geometric properties of lyapunov equation and lti system while many algebraic properties of lyapunov equation and lti system are well known few geometric properties which may be used to analyze control system properties are studied in this paper some new necessary and sufficient conditions based on geometry are derived for properties of the lyapunov equation and lti system

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

occupation times of hyper exponential jump diffusion processes with application to price step options we are interested in occupation times of jump diffusion processes with hyper exponentially distributed jump sizes we develop a new approach to derive analytical formulas for the laplace transform of the joint distribution of a hyper exponential jump diffusion process and its occupation times these formulas are then used to price step options

a survey of adaptive fuzzy controllers nonlinearities and classifications adaptive fuzzy controllers afcs i e fuzzy controllers using heuristic expert knowledge and equipped with adaption ability are widely used in the industry in the present days as they are capable of dealing with ill formulated nonlinear systems where exact mathematical formulas are not known or partially described nonlinear systems afcs have been widely deployed to control many nonlinear systems with different types of critical nonlinearities over the last two decades many different approaches toward adaptive fuzzy control have been reported in this paper we recapitulate the latest research works related to afcs and provide an up to date survey on the latest development made in adaptive fuzzy control theory and applications based on different types of fuzzy systems considered and nonlinearities associated with the nonlinear system to be controlled we categorize the different approaches based on different types of nonlinearities and consider basic nonlinear systems nonlinear systems with external disturbances nonlinear systems with some special type of nonlinearities nonaffine nonlinear systems and strict feedback nonlinear systems it turns out that many existing methods are subject to various limitations and none of them is capable of controlling a general nonlinear systems hence it is still an open problem to design and develop a universal afc for a general class of nonlinear systems

an rbf fd method for pricing american options under jump diffusion models abstract american option prices under jump diffusion models are determined as solutions to partial integro differential equations pide in this paper a new combination of a time and spatial discretization applied to a linear complementary formulation lcp of the free boundary pide is proposed first a coordinate stretching transformation is performed to the asset price so that the computation of the prices can be focused on regions of real interest instead of on the whole solution domain an implicit explicit time discretization applied to the reformulated lcp on a uniform temporal grid is followed by a spatial discretization to get a fully discrete system the radial basis function rbf finite difference method is a local method resulting in a sparse linear system in contrast to global rbf methods which lead to ill conditioned dense matrix systems for the corresponding european option we prove consistency stability and second order convergence in a discrete l 2 norm we derive mild conditions for the model parameters under which these results hold numerical experiments are performed with european and american options and a comparison with numerical results available in the literature illustrates the accuracy and efficiency of the proposed algorithm

boosting textual compression in optimal linear time we provide a general boosting technique for textual data compression qualitatively it takes a good compression algorithm and turns it into an algorithm with a better compression performance guarantee it displays the following remarkable properties a it can turn any memoryless compressor into a compression algorithm that uses the best possible contexts b it is very simple and optimal in terms of time and c it admits a decompression algorithm again optimal in time to the best of our knowledge this is the first boosting technique displaying these properties technically our boosting technique builds upon three main ingredients the burrows wheeler transform the suffix tree data structure and a greedy algorithm to process them specifically we show that there exists a proper partition of the burrows wheeler transform of a string s that shows a deep combinatorial relation with the kth order entropy of s that partition can be identified via a greedy processing of the suffix tree of s with the aim of minimizing a proper objective function over its nodes the final compressed string is then obtained by compressing individually each substring of the partition by means of the base compressor we wish to boost our boosting technique is inherently combinatorial because it does not need to assume any prior probabilistic model about the source emitting s and it does not deploy any training parameter estimation and learning various corollaries are derived from this main achievement among the others we show analytically that using our booster we get better compression algorithms than some of the best existing ones that is lz77 lz78 ppmc and the ones derived from the burrows wheeler transform further we settle analytically some long standing open problems about the algorithmic structure and the performance of bwt based compressors namely we provide the first family of bwt algorithms that do not use move to front or symbol ranking as a part of the compression process

stock trading an optimal selling rule trading in stock markets consists of three major steps select a stock purchase a number of shares and eventually sell them to make a profit the timing to buy and sell is extremely crucial a selling rule can be specified by two preselected levels a target price and a stop loss limit this paper is concerned with an optimal selling rule based on the model characterized by a number of geometric brownian motions coupled by a finite state markov chain such a policy can be obtained by solving a set of two point boundary value differential equations moreover the corresponding expected target period and probability of making money and that of losing money are derived analytic solutions are obtained in one and two dimensional cases finally a numerical example is considered to demonstrate the effectiveness of our method

convergence of numerical schemes for viscosity solutions to integro differential degenerate parabolic problems arising in financial theory we study the numerical approximation of viscosity solutions for integro differential possibly degenerate parabolic problems similar models arise in option pricing to generalize the celebrated black scholes equation when the processes which generate the underlying stock returns may contain both a continuous part and jumps convergence is proven for monotone schemes and numerical tests are presented and discussed

hybrid filtering for linear systems with non gaussian disturbances this paper is concerned with hybrid filtering of a non gaussian system coupled by a hidden switching process an optimal control approach is used to derive a finite dimensional recursive filter that is optimal in the sense of the most probable trajectory mpt estimate an approximate scheme is obtained when the probability distribution of the switching process converges to a limiting distribution which is often easier to obtain numerical examples are considered and computational experiments are reported in these examples our schemes outperform popular filtering schemes available in the literature

computation of convex bounds for present value functions with random payments in this contribution we study the distribution of the present value function of a series of random payments in a stochastic financial environment such distributions occur naturally in a wide range of applications within fields of insurance and finance we obtain accurate approximations by developing upper and lower bounds in the convex order sense for present value functions technically speaking our methodology is an extension of the results of dhaene et al insur math econom 31 1 2002 3 33 insur math econom 31 2 2002 133 161 to the case of scalar products of mutually independent random vectors

adaptive neural tracking control for a class of nonstrict feedback stochastic nonlinear systems with unknown backlash like hysteresis this paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict feedback form with unknown backlash like hysteresis nonlinearities to overcome the design difficulty of nonstrict feedback structure variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic by combining radial basis function neural networks universal approximation capability with an adaptive backstepping technique an adaptive neural control algorithm is proposed it is shown that the proposed controller guarantees that all the signals in the closed loop system are four moment semiglobally uniformly ultimately bounded and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value simulation results further show the effectiveness of the presented control scheme

nonlinear filtering and control of a switching diffusion with small observation noise this paper is concerned with nonlinear filtering and control of a switching diffusion coupled by an unknown markov chain two statistical estimation methods are used to track the unknown markov chain computable approximate filters are obtained based on these methods the filters are then used to construct controls for the partially observed system these controls are shown to be asymptotically optimal as the observation noise tends to zero finally an example is considered and numerical experiments are reported

relative degrees and adaptive feedback linearization control of t s fuzzy systems this paper presents a new study on the relative degrees of single input and single output t s fuzzy systems in general noncanonical forms and proposes a feedback linearization based control design method for such systems the study extends the system relative degree concepts commonly used for the control of nonlinear systems to general t s fuzzy systems derives various relative degree conditions for general t s fuzzy systems and establishes the relative degree dependent normal forms a feedback linearization based control design framework is developed for general t s fuzzy systems using its normal form to achieve closed loop stability and asymptotic output tracking under relaxed design conditions a new adaptive feedback linearization based control scheme for t s fuzzy systems in general noncanonical forms with parameter uncertainties is designed and analyzed some extensions of relative degrees and their possible application to robust adaptive control for noncanonical form t s fuzzy systems are also demonstrated an illustrative example is presented with simulation results to demonstrate the control system design procedure and to show the effectiveness of the proposed control scheme

limit at zero of the brownian first passage density let b t t 0 be a standard brownian motion started at zero let g be an upper function for b satisfying g 0 0 and let be the first passage time of b over g assume that g is c 1 on increasing locally at zero and concave locally at zero then the following identities hold for the density function f of in the sense that if the second and third limit exist so does the first one and the equalities are valid here is the standard normal density these limits can take any value in 0 the method of proof relies upon the strong markov property of b and makes use of real analysis

first passage times of two dimensional correlated processes given a two dimensional correlated diffusion process we determine the joint density of the first passage times of the process to some constant boundaries this quantity depends on the joint density of the first passage time of the first crossing component and of the position of the second crossing component before its crossing time first we show that these densities are solutions of a system of volterra fredholm first kind integral equations then we propose a numerical algorithm to solve it and we describe how to use the algorithm to approximate the joint density of the first passage times the convergence of the method is theoretically proved for bivariate diffusion processes we derive explicit expressions for these and other quantities of interest in the case of a bivariate wiener process correcting previous misprints appearing in the literature finally we illustrate the application of the method through a set of examples

bounds for the price of discrete arithmetic asian options in this paper the pricing of european style discrete arithmetic asian options with fixed and floating strike is studied by deriving analytical lower and upper bounds in our approach we use a general technique for deriving upper and lower bounds for stop loss premiums of sums of dependent random variables as explained in kaas et al ins math econom 27 2000 151 168 and additionally the ideas of rogers and shi j appl probab 32 1995 1077 1088 and of nielsen and sandmann j financial quant anal 38 2 2003 449 473 we are able to create a unifying framework for european style discrete arithmetic asian options through these bounds that generalizes several approaches in the literature as well as improves the existing results we obtain analytical and easily computable bounds the aim of the paper is to formulate an advice of the appropriate choice of the bounds given the parameters investigate the effect of different conditioning variables and compare their efficiency numerically several sets of numerical results are included we also discuss hedging using these bounds moreover our methods are applicable to a wide range of pricing problems involving a sum of dependent random variables

a first passage problem for a bivariate diffusion process numerical solution with an application to neuroscience when the process is gauss markov we consider a bivariate gauss markov process and we study the first passage time of one component through a constant boundary we prove that its probability density function is the unique solution of a new integral equation and we propose a numerical algorithm for its solution convergence properties of this algorithm are discussed and the method is applied to the study of the integrated brownian motion and to the integrated ornstein uhlenbeck process finally a model of neuroscience interest is discussed

succinct representation of balanced parentheses and static trees we consider the implementation of abstract data types for the static objects binary tree rooted ordered tree and a balanced sequence of parentheses our representations use an amount of space within a lower order term of the information theoretic minimum and support in constant time a richer set of navigational operations than has previously been considered in similar work in the case of binary trees for instance we can move from a node to its left or right child or to the parent in constant time while retaining knowledge of the size of the subtree at which we are positioned the approach is applied to produce a succinct representation of planar graphs in which one can test adjacency in constant time

numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric levy motion abstract for non gaussian stochastic dynamical systems mean exit time and escape probability are important deterministic quantities which can be obtained from integro differential nonlocal equations we develop an efficient and convergent numerical method for the mean first exit time and escape probability for stochastic systems with an asymmetric levy motion and analyze the properties of the solutions of the nonlocal equations the discretized equation has toeplitz structure that enables utilization of fast fourier transform in numerical simulations we also investigate the effects of different system factors on the mean exit time and escape probability including the skewness parameter the size of the domain the drift term and the intensity of gaussian and non gaussian noises we find that the behavior of the mean exit time and the escape probability has dramatic difference at the boundary of the domain when the index of stability crosses the critical value of one

comonotonic approximations for a generalized provisioning problem with application to optimal portfolio selection in this paper we discuss multiperiod portfolio selection problems related to a specific provisioning problem our results are an extension of dhaene et al 2005 14 where optimal constant mix investment strategies are obtained in a provisioning and savings context using an analytical approach based on the concept of comonotonicity we derive convex bounds that can be used to estimate the provision to be set up at a specified time in future to ensure that after having paid all liabilities up to that moment all liabilities from that moment on can be fulfilled with a high probability

on barrier option pricing by erlangization in a regime switching model with jumps abstract we consider the risk neutral pricing of vanilla digital and down and out call options when the underlying asset price evolves like the exponential of a markov modulated brownian motion mmbm with two sided phase type jumps the price of such options is intimately related to the first passage properties of the mmbm to analyse these first passages we randomize the time horizon using erlang distributions with suitable parameters and apply matrix analytic methods this provides us with closed form approximations of the options prices with a very high precision as shown by several numerical illustrations in particular we consider an example in which the phase type jump distribution is constructed in such a way that it mimics fat tails

phase type fitting of scale functions for spectrally negative levy processes we study the scale function of the spectrally negative phase type levy process its scale function admits an analytical expression and so do a number of its fluctuation identities motivated by the fact that the class of phase type distributions is dense in the class of all positive valued distributions we propose a new approach to approximating the scale function and the associated fluctuation identities for a general spectrally negative levy process numerical examples are provided to illustrate the effectiveness of the approximation method

continuous time adaptive control of systems with unknown backlash this paper addresses one of the nondifferentiable nonlinearities which appear very often in industrial control applications backlash the authors first present a right inverse of backlash and then give one of its possible implementations characteristics like backlash are seldom known so an adaptive version of the authors backlash inverse is more suitable for applications the authors develop an adaptive backlash inverse scheme and apply it to feedback control of a known linear plant with an unknown backlash at its input the authors use simulation results to illustrate achieved performance improvements

asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented we consider two possible input nonlinearities that is backlash like hysteresis and symmetric dead zone which can be simultaneously dealt with by using the proposed compensation controllers the knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required only the boundedness of the reference signal is assumed the nussbaum gain approach is employed to remove the assumption on the control gain sign the first scheme is based on the backstepping technique the final step of the recursive design is crucial for the closed loop stability in the second scheme a direct adaptive control law is designed the controller has a simple structure and only one adaptation parameter is updated in both controllers it is shown that asymptotic tracking is ensured two numerical examples are provided to show the effectiveness of the theor

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

comonotonic approximations of risk measures for variable annuity guaranteed benefits with dynamic policyholder behavior the computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed benefits the current market practice of monte carlo simulation often requires intensive computations which can be very costly for insurance companies to implement and take so much time that they cannot obtain information and take actions in a timely manner in an attempt to find low cost and efficient alternatives we explore the techniques of comonotonic bounds to produce closed form approximation of risk measures for variable annuity guaranteed benefits the techniques are further developed in this paper to address in a systematic way risk measures for death benefits with the consideration of dynamic policyholder behavior which involves very complex path dependent structures in several numerical examples the method of comonotonic approximation is shown to run several thousand times faster than simulations with only minor compromise of accuracy

adaptive fuzzy output feedback control of mimo nonlinear systems with unknown dead zone inputs this paper is concerned with the problem of adaptive fuzzy tracking control for a class of multi input and multi output mimo strict feedback nonlinear systems with both unknown nonsymmetric dead zone inputs and immeasurable states in this research fuzzy logic systems are utilized to evaluate the unknown nonlinear functions and a fuzzy adaptive state observer is established to estimate the unmeasured states based on the information of the bounds of the dead zone slopes as well as treating the time varying inputs coefficients as a system uncertainty a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique it is shown that the proposed control approach can assure that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded it is also shown that the observer and tracking errors converge to a small neighborhood of the origin by selecting appropriate design parameters simulation examples are also provided to illustrate the effectiveness of the proposed approach

the re nonnegative definite and re positive definite solutions to the matrix equation axb d in this paper the re nonnegative definite re nnd and re positive definite re pd solutions of the matrix equation axb d are considered the necessary and sufficient conditions for the existence of re nnd and re pd solutions to the equation are provided and the explicit representations of the general re nnd and re pd solutions are given when it is solvable

an imex scheme for pricing options under stochastic volatility models with jumps partial integro differential equation pide formulations are often preferable for pricing options under models with stochastic volatility and jumps especially for american style option contracts we consider the pricing of options under such models namely the bates model and the so called stochastic volatility with contemporaneous jumps svcj model the nonlocality of the jump terms in these models leads to matrices with full matrix blocks standard discretization methods are not viable directly since they would require the inversion of such a matrix instead we adopt a two step implicit explicit imex time discretization scheme the imex cnab scheme where the jump term is treated explicitly using the second order adams bashforth ab method while the rest is treated implicitly using the crank nicolson cn method the resulting linear systems can then be solved directly by employing lu decomposition alternatively the systems can be iterated under a scalable algebraic multigrid amg method f

adaptive fuzzy output feedback tracking backstepping control of strict feedback nonlinear systems with unknown dead zones in this paper an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict feedback systems with unknown functions unknown dead zones and immeasurable states fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy filters state observer is designed to estimate the immeasurable states by using the adaptive backstepping recursive design technique and constructing the dead zone inverse a new adaptive fuzzy backstepping output feedback control approach is developed it is mathematically proved that all the signals of the resulting closed loop adaptive control system are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters the proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement two simulation examples are provided to show the effectiveness of the proposed approach

on compressing permutations and adaptive sorting we prove that given a permutation p over 1 n formed of nruns sorted blocks of sizes given by the vector r there exists a compressed data structure encoding p in n 1 h r n i 1 n r u n sr ilog 2nr i

mathematical models for hysteresis the various existing classical models for hysteresis preisach ishlinskii duhem madelung are surveyed as well a more modern treatments by contemporary workers the emphasis is on a clear mathematical description of the formulation and properties of each model in addition the authors try to make the reader aware of the many open questions in the study of hysteresis

adaptive fuzzy output feedback control of uncertain nonlinear systems with unknown backlash like hysteresis in this paper the problem of adaptive fuzzy output feedback control is investigated for a class of uncertain nonlinear systems with unknown backlash like hysteresis and unmeasured states the fuzzy logic systems are used to approximate the nonlinear system functions and a fuzzy state observer is designed to estimate the unmeasured states by utilizing the fuzzy state observer and combining the adaptive backstepping technique with adaptive fuzzy control design an observer based adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that all the signals in the closed loop system are semi globally uniformly ultimately bounded suub and both observer error and tracking error can converge to a small neighborhood of the origin two simulations are included to illustrate the effectiveness of the proposed approach

a second order finite difference method for option pricing under jump diffusion models we develop a finite difference method to solve partial integro differential equations which describe the behavior of option prices under jump diffusion models with localization to a bounded domain of the spatial variable these equations are discretized on uniform grid points over a finite domain of time and spatial variables the proposed method is based on three time levels and leads to linear systems with tridiagonal matrices in this paper the stability of the proposed method and the second order convergence rate with respect to a discrete ell 2 norm are proved numerical results obtained with european put options under the merton and kou models show the behaviors of the stability and the second order convergence rate

adaptive control of a class of nonlinear systems with fuzzy logic an adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture employs fuzzy systems which are expressed as a series expansion of basis functions to adaptively compensate for the plant nonlinearities global asymptotic stability of the algorithm is established in the lyapunov sense with tracking errors converging to a neighborhood of zero simulation results for an unstable nonlinear plant are included to demonstrate that incorporating the linguistic fuzzy information from human experts results in superior tracking performance

adaptive fuzzy control for a class of stochastic pure feedback nonlinear systems with unknown hysteresis this paper addresses the problem of adaptive fuzzy control for a class of stochastic pure feedback nonlinear systems with unknown direction hysteresis compared with the existing researches on hysteresis problem the stochastic disturbances and the unknown hysteresis are simultaneously considered in the pure feedback systems in addition the hysteresis parameters as well as the direction of hysteresis are unknown by introducing an auxiliary virtual controller and employing the new properties of nussbaum function the major technique difficulty arising from the unknown direction hysteresis is overcome based on the fuzzy logic system s online approximation capability a novel adaptive fuzzy control scheme is presented via the backstepping technique it is shown that the proposed control scheme guarantees that all the signals of the closed loop system are semiglobally uniformly bounded in probability and the tracking error converges to a neighborhood of the origin in the sense of mean quantic value finally simulation results further demonstrate the effectiveness of the proposed control scheme

rbf pu method for pricing options under the jump diffusion model with local volatility abstract meshfree methods based on radial basis functions rbfs are of general interest for solving partial differential equations pdes because they can provide high order or spectral convergence for smooth solutions in complex geometries for global rbf methods one of the major disadvantages is the computational cost associated with the dense linear systems that arise therefore this paper is currently directed toward localized rbf approximations known as the rbf partition of unity rbf pu method for partial integro differential equation pide arisen in option pricing problems in jump diffusion model rbf pu method produces algebraic systems with sparse matrices which have small condition number also for comparison some stable time discretization schemes are combined with the operator splitting method to get a fully discrete problem numerical examples are presented to illustrate the convergence and stability of the proposed algorithms for pricing european and american options with merton and kou models

optimal approximations for risk measures of sums of lognormals based on conditional expectations in this paper we investigate the approximations for the distribution function of a sum s of lognormal random variables these approximations are obtained by considering the conditional expectation e s l of s with respect to a conditioning random variable l the choice of l is crucial in order to obtain accurate approximations the different alternatives for l that have been proposed in the literature to date are global in the sense that l is chosen such that the entire distribution of the approximation e s l is close to the corresponding distribution of the original sum s in an actuarial or a financial context one is often only interested in a particular tail of the distribution of s therefore in this paper we propose approximations e s l which are only locally optimal in the sense that the relevant tail of the distribution of e s l is an accurate approximation for the corresponding tail of the distribution of s numerical illustrations reveal that local optimal choices for l can improve the quality of the approximations in the relevant tail significantly we also explore the asymptotic properties of the approximations e s l and investigate links with results from s asmussen rojas nandayapa sums of dependent lognormal random variables asymptotics and simulation stochastic series at department of mathematical sciences university of aarhus research report number 469 2005 finally we briefly address the sub optimality of asian options from the point of view of risk averse decision makers with a fixed investment horizon

observer based adaptive fuzzy tracking control of mimo stochastic nonlinear systems with unknown control directions and unknown dead zones in this paper an adaptive fuzzy backstepping output feedback tracking control approach is proposed for a class of multi input and multi output mimo stochastic nonlinear systems the mimo stochastic nonlinear systems under study are assumed to possess unstructured uncertainties unknown dead zones and unknown control directions by using a linear state transformation the unknown control coefficients and the unknown slopes characteristic of the dead zones are lumped together and the original system is transformed to a new system on which the control design becomes feasible fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by introducing a special nussbaum gain function into the backstepping control design a stable adaptive fuzzy output feedback tracking control scheme is developed the main features of the proposed adaptive control approach are that it can guarantee the stability of the closed loop system and the tracking errors converge to a small neighborhood of zero moreover it can solve the problems of unknown control direction unknown dead zone and unmeasured states simultaneously two simulation examples are provided to show the effectiveness of the proposed approach

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

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

robust adaptive control of a class of nonlinear systems with unknown backlash like hysteresis deals with adaptive control of a class of nonlinear dynamic systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is modeled by a differential equation by exploiting solution properties of the differential equation and combining those properties with adaptive control techniques a robust adaptive control algorithm is developed without constructing a hysteresis inverse the new control law ensures global stability of the adaptive system and achieves both stabilization and tracking to within a desired precision simulations performed on a nonlinear system illustrate and clarify the approach

european option pricing under stochastic volatility jump diffusion models with transaction cost abstract in this paper we consider an underlying general stochastic volatility jump diffusion model option pricing under this general model with transaction costs will lead to handling with nonlinear partial integro differential equations here after pide in this case option replication in a discrete time framework with transaction costs and the non uniqueness option pricing in such incomplete market will be studied observing and introducing a traded proxy for the volatility in the modern market we acquire a nonlinear pide in the advent of transaction costs under appropriate regularity conditions the existence of the strong solution to this pricing problem has been proved the corresponding self financing and positions readjustment for pricing a portfolio will also be discussed in the end

closed form solutions for perpetual american put options with regime switching this paper studies an optimal stopping time problem for pricing perpetual american put options in a regime switching model an explicit optimal stopping rule and the corresponding value function in a closed form are obtained using the modified smooth fit technique the solution is then compared with the numerical results obtained via a dynamic programming approach and also with a two point boundary value differential equation tpbvde method

stable adaptive fuzzy control of nonlinear systems preceded by unknown backlash like hysteresis this paper deals with adaptive control of nonlinear dynamic systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is described by a dynamic equation by utilizing this dynamic model and by combining a fuzzy universal function approximator with adaptive control techniques a stable adaptive fuzzy control algorithm is developed without constructing a hysteresis inverse the stability of the closed loop system is shown using lyapunov arguments the effectiveness of the proposed method is demonstrated through simulations

a finite difference scheme for option pricing in jump diffusion and exponential levy models we present a finite difference method for solving parabolic partial integro differential equations with possibly singular kernels which arise in option pricing theory when the random evolution of the underlying asset is driven by a levy process or more generally a time inhomogeneous jump diffusion process we discuss localization to a finite domain and provide an estimate for the localization error under an integrability condition on the levy measure we propose an explicit implicit finite difference scheme which can be used to price european and barrier options in such models we study stability and convergence of the scheme proposed and under additional conditions provide estimates on the rate of convergence numerical tests are performed with smooth and nonsmooth initial conditions

efficient and compact representations of prefix codes most of the attention in statistical compression is given to the space used by the compressed sequence a problem completely solved with optimal prefix codes however in many applications the storage space used to represent the prefix code itself can be an issue in this paper we introduce and compare several techniques to store prefix codes let n be the sequence length and n be the alphabet size then a naive storage of an optimal prefix code uses mathcal o hspace 5ex left n log n right bits our first technique shows how to use mathcal o hspace 5ex left n log log n n right bits to store the optimal prefix code then we introduce an approximate technique that for any 0 takes mathcal o hspace 5ex left n log log 1 epsilon right bits to store a prefix code with an average codeword length within an additive epsilon of the minimum finally a second approximation takes for any constant c 1 vphantom sum r r mathcal o n 1 c log n bits to store a prefix code with an average codeword length at most c times the minimum in all cases our data structures allow encoding and decoding of any symbol in mathcal o hspace 5ex left 1 right time we experimentally compare our new techniques with the state of the art showing that we achieve sixfold to eightfold space reductions at the price of a slower encoding 2 5 8 times slower and decoding 12 24 times slower the approximations further reduce this space and improve the time significantly up to recovering the speed of classical implementations for a moderate penalty in the average code length as a byproduct we compare various heuristic approximate and optimal algorithms to generate length restricted codes showing that the optimal ones are clearly superior and practical enough to be implemented

tridiagonal implicit method to evaluate european and american options under infinite activity levy models we propose an efficient implicit method to evaluate european and american options when the underlying asset follows an infinite activity levy model since the levy measure of the infinite activity model has the singularity at the origin we approximate infinitely many small jumps by samples of a diffusion the proposed methods to solve partial integro differential equations for european options and linear complementarity problems for american options via an operator splitting method involve solving linear systems with tridiagonal matrices and so can significantly reduce the computations associated with the discrete integral operators the numerical experiments verify that the proposed method has the second order convergence rate under an infinite activity levy model

a note on hurwitz stability of matrices this note proves that every hurwitz stable matrix can be expressed as the product of a symmetric positive definite matrix and a generalised negative definite matrix based on this it is further shown that the entire set of all hurwitz stable matrices of order n is the product of two convex open cones and itself forms a simply connected open cone in the parameter space with a vertex at the origin

estimating the gerber shiu function in the perturbed compound poisson model by laguerre series expansion abstract in this paper we study the statistical estimation of the gerber shiu function in the compound poisson risk model perturbed by diffusion this problem has been solved in 32 by the fourier sinc series expansion method different from 32 we use the laguerre series to expand the gerber shiu function and propose a relevant estimator the estimator is easily computed and has fast convergence rate various simulation studies are presented to confirm that the estimator performs well when the sample size is finite

a fast algorithm for the first passage times of gauss markov processes with holder continuous boundaries even for simple diffusion processes treating first passage problems analytically proves intractable for generic barriers and existing numerical methods are inaccurate and computationally costly here we present a novel numerical method that is faster and has more tightly controlled accuracy our algorithm is a probabilistic variant of dichotomic search for the computation of first passage times through non negative homogeneously holder continuous boundaries by gauss markov processes these include the ornstein uhlenbeck process underlying the ubiquitous leaky integrate and fire model of neuronal excitation our method evaluates discrete points in a sample path exactly and refines this representation recursively only in regions where a passage is rigorously estimated to be probable e g when close to the boundary