european option pricing with transaction costs the authors consider the problem of pricing european options in a market model similar to the black scholes one except that proportional transaction charges are levied on all sales and purchases o

inversion of polynomial systems and separation of nonlinear mixtures of finite alphabet sources in this contribution multiple input multiple output mimo mixing systems are considered which are instantaneous and nonlinear but polynomial we first address the problem of invertibility searching the inverse in the class of polynomial systems it is shown that grobner bases techniques offer an attractive solution for testing the existence of an exact inverse and computing it by noticing that any nonlinear mapping can be interpolated by a polynomial on a finite set we tackle the general nonlinear case relying on a finite alphabet assumption of the input source signals theoretical results on polynomials allow us to represent nonlinear systems as linear combinations of a finite set of monomials we then generalize the first results to give a condition for the existence of an exact nonlinear inverse the proposed method allows to compute this inverse in polynomial form in the light of the previous results we go further to the blind source separation problem it is shown that for sources in a finite alphabet the nonlinear problem is tightly connected with both problems of under determination and of dependent sources we concentrate on the case of two binary sources for which an easy solution can be found by simulation this solution is compared to techniques borrowed from classification methods

a singular boundary value problem for the one dimensionalp laplacian abstract the singular boundary value problem formula is studied in this paper whereg s s p 2s p 1 the singularity may appear atu 0 and att 0 ort 1 and the functionfmay be discontinuous the authors prove that for anyp 1 and for any positive nonincreasing functionfand nonnegative measurable functionkwith some integrability conditions the above mentioned problem has a unique solution also the properties of the solution are discussed in the paper

singular boundary value problems on a half line singular boundary value problems of nonlinear second order differential equations on a half line are considered the main methods used are modified upper and lower solution techniques necessary and sufficient conditions for the existence of solutions to a class of sublinear singular boundary value problems are obtained

penalty approach to a nonlinear obstacle problem governing american put option valuation under transaction costs we propose a penalty method for a finite dimensional nonlinear complementarity problem ncp arising from the discretization of the infinite dimensional free boundary obstacle problem governing the valuation of american options under transaction costs in this method the ncp is approximated by a system of nonlinear equations containing a power penalty term we show that the mapping involved in the system is continuous and strongly monotone thus the unique solvability of both the ncp and the penalty equation and the exponential convergence of the solution to the penalty equation to that of the ncp are guaranteed by an existing theory numerical results will be presented to demonstrate the convergence rates and usefulness of this penalty method

singular boundary value problems for superlinear second order ordinary and delay differential equations abstract existence criteria are established for singular boundary value problems for nonlinear second order ordinary and delay differential equations the theorems obtained are very general and complement previous known results

frame theoretic analysis of oversampled filter banks we provide a frame theoretic analysis of oversampled finite impulse response fir and infinite impulse response fir uniform filter banks fbs our analysis is based on a new relationship between the fbs polyphase matrices and the frame operator corresponding to an fb for a given oversampled analysis fb we present a parameterization of all synthesis fbs providing perfect reconstruction we find necessary and sufficient conditions for an oversampled fb to provide a frame expansion a new frame theoretic procedure for the design of paraunitary fbs from given nonparaunitary fbs is formulated we show that the frame bounds of an fb can be obtained by an eigen analysis of the polyphase matrices the relevance of the frame bounds as a characterization of important numerical properties of an fb is assessed by means of a stochastic sensitivity analysis we consider special cases in which the calculation of the frame bounds and synthesis filters is simplified finally simulation results are presented

pricing european options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme abstract in this paper we propose a combination of a penalty method and a finite volume scheme for a four dimensional time dependent hamilton jacobi bellman hjb equation arising from pricing european options with proportional transaction costs and stochastic volatility the hjb equation is first approximated by a nonlinear partial differential equation containing penalty terms a finite volume method along with an upwind technique is then developed for the spatial discretization of the nonlinear penalty equation we show that the coefficient matrix of the discretized system is an m matrix an iterative method is proposed for solving the nonlinear algebraic system and a convergence theory is established for the iterative method numerical experiments are performed using a non trivial model pricing problem and the numerical results demonstrate the usefulness of the proposed method

twin solutions to singular dirichlet problems the existence of two nonnegative solutions to dirichlet second order boundary value problems is established in this paper our nonlinearity may be singular at y 0 t 0 and or t 1

on the numerical solution of nonlinear black scholes equations nonlinear black scholes equations have been increasingly attracting interest over the last two decades since they provide more accurate values by taking into account more realistic assumptions such as transaction costs risks from an unprotected portfolio large investor s preferences or illiquid markets which may have an impact on the stock price the volatility the drift and the option price itself in this paper we will focus on several models from the most relevant class of nonlinear black scholes equations for european and american options with a volatility depending on different factors such as the stock price the time the option price and its derivatives due to transaction costs we will analytically approach the option price by transforming the problem for a european call option into a convection diffusion equation with a nonlinear term and the free boundary problem for an american call option into a fully nonlinear nonlocal parabolic equation defined on a fixed domain following sevcovic s idea finally we will present the results of different numerical discretization schemes for european options for various volatility models including the leland model the barles and soner model and the risk adjusted pricing methodology model

oversampled filter banks perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l sup 2 z these frames are the subject of this paper first the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established as well as a necessary and sufficient condition for perfect reconstruction using fir filters after an fir analysis complete parameterizations of oversampled filter banks satisfying these conditions are given further we study the condition under which the frame dual to the frame associated with an fir filter bank is also fir and give a parameterization of a class of filter banks satisfying this property then we focus on non subsampled filter banks non subsampled filter banks implement transforms similar to continuous time transforms and allow for very flexible design we investigate the relations of these filter banks to continuous time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two channel filter banks that yield highly regular wavelets with a given number of vanishing moments

multiple positive solutions of some boundary value problems abstract we study the existence of multiple positive solutions of the equations u t u subject to linear boundary conditions we show that there are at least two positive solutions if t u is superlinear at one end point zero or infinity and sublinear at the other applications of these results are provided to yield multiple positive solutions of some elliptic boundary value problems on an annulus

sharp effective nullstellensatz the usual proofs of this result however give no information about the g1 s for instance they give no bound on their degrees this question was first considered by g hermann h she used elimination theory to get a bound on the degree of the gi s which was doubly exponential in the number of variables her results were later improved in mw and in th all these produce bounds that are doubly exponential in the number of variables a major breakthrough was achieved by brownawell b1 who proved the following result

multidimensional filter bank signal reconstruction from multichannel acquisition we study the theory and algorithms of an optimal use of multidimensional signal reconstruction from multichannel acquisition by using a filter bank setup suppose that we have an channel convolution system referred to as analysis filters in dimensions instead of taking all the data and applying multichannel deconvolution we first reduce the collected data set by an integer uniform sampling matrix and then search for a synthesis polyphase matrix which could perfectly reconstruct any input discrete signal first we determine the existence of perfect reconstruction pr systems for a given set of finite impulse response fir analysis filters second we present an efficient algorithm to find a sampling matrix with maximum sampling rate and to find a fir pr synthesis polyphase matrix for a given set of fir analysis filters finally once a particular fir pr synthesis polyphase matrix is found we can characterize all fir pr synthesis matrices and then find an optimal one according to design criteria including robust reconstruction in the presence of noise

a filter algorithm for nonlinear systems of equalities and inequalities abstract in this paper we propose a filter algorithm for nonlinear systems of equalities and inequalities in the algorithm the systems of nonlinear equalities and inequalities are transformed into a nonlinear programming problem the new algorithm uses the non monotone technique in conjunction with filter idea and a global line search strategy that ensures convergence from any starting point under mild conditions global convergence and local superlinear convergence rate are obtained numerical results demonstrate that the new algorithm is effective

exact image deconvolution from multiple fir blurs we address the problem of restoring an image from its noisy convolutions with two or more blur functions channels deconvolution from multiple blurs is in general better conditioned than from a single blur and can be performed without regularization for moderate noise levels we characterize the problem of missing data at the image boundaries and show that perfect reconstruction is impossible even in the no noise case almost surely unless there are at least three channels conversely when there are at least three channels we show that perfect reconstruction is not only possible almost surely in the absence of noise but also that it can be accomplished by finite impulse response fir filtering such fir reconstruction is vastly more efficient computationally than the least squares solution and is suitable for low noise levels even in the high noise case the estimates obtained by fir filtering provide useful starting points for iterative least squares algorithms we present results on the minimum possible sizes of such deconvolver filters we derive expressions for the mean square errors in the fir reconstructions and show that performance comparable to that of the least squares reconstruction may be obtained with relatively small deconvolver filters finally we demonstrate the fir reconstruction on synthetic and real data

pricing american bond options using a penalty method we develop a novel numerical method to price american options on a discount bond under the cox ingrosll ross cir model which is governed by a partial differential complementarity problem we first propose a penalty approach to this complementarity problem resulting in a nonlinear partial differential equation pde to numerically solve this nonlinear pde we develop a novel fitted finite volume method for the spatial discretization coupled with a fully implicit time stepping scheme we show that this full discretization scheme is consistent stable and monotone and hence the convergence of the numerical solution to the viscosity solution of the continuous problem is guaranteed to solve the discretized nonlinear system we design an iterative method and prove that the method is convergent numerical results are presented to demonstrate the accuracy efficiency and robustness of our methods

multidimensional multichannel fir deconvolution using grobner bases we present a new method for general multidimensional multichannel deconvolution with finite impulse response fir convolution and deconvolution filters using grobner bases previous work formulates the problem of multichannel fir deconvolution as the construction of a left inverse of the convolution matrix which is solved by numerical linear algebra however this approach requires the prior information of the support of deconvolution filters using algebraic geometry and grobner bases we find necessary and sufficient conditions for the existence of exact deconvolution fir filters and propose simple algorithms to find these deconvolution filters the main contribution of our work is to extend the previous grobner basis results on multidimensional multichannel deconvolution for polynomial or causal filters to general fir filters the proposed algorithms obtain a set of fir deconvolution filters with a small number of nonzero coefficients a desirable feature in the impulsive noise environment and do not require the prior information of the support moreover we provide a complete characterization of all exact deconvolution fir filters from which good fir deconvolution filters under the additive white noise environment are found simulation results show that our approaches achieve good results under different noise settings

generic invertibility of multidimensional fir filter banks and mimo systems in this paper we study the invertibility of m variate laurent polynomial n times p matrices such matrices represent multidimensional systems in various settings such as filter banks multiple input multiple output systems and multirate systems given an n times p laurent polynomial matrix h z1 zm of degree at most k we want to find a p times n laurent polynomial left inverse matrix g z of h z such that g z h z j we provide computable conditions to test the invertibility and propose algorithms to find a particular inverse the main result of this paper is to prove that h z is generically invertible when n p ges m whereas when n p m then h z is generically noninvertible as a result we propose an algorithm to find a particular inverse of a laurent polynomial matrix that is faster than current algorithms known to us

an upwind finite difference method for a nonlinear black scholes equation governing european option valuation under transaction costs in this paper we develop a numerical method for a nonlinear parabolic partial differential equation arising from pricing european options under transaction costs the method is based on an upwind finite difference scheme for the spatial discretization and a fully implicit time stepping scheme we prove that the system matrix from this scheme is an m matrix and that the approximate solution converges unconditionally to the viscosity solution to the equation by showing that the scheme is consistent monotone and unconditionally stable a newton iterative algorithm is proposed for solving the discretized nonlinear system of which the jacobian matrix is shown to be also an m matrix numerical experiments are performed to demonstrate the accuracy and robustness of the method

solvability of some nonlinear boundary value problems on etablit l existence des solutions positives de problemes a deux points limites singuliers pour des equations differentielles de la forme y f t y y o o t 1

fir perfect signal reconstruction from multiple convolutions minimum deconvolver orders given p co prime finite impulse response fir filters h sub i spl isin r m sub h it well known that there exist q sub i spl isin r m sub q such that spl sigma sub i h sub i q sub i spl delta importantly this enables signal recovery from its convolutions with p spl ges 2 co prime fir filters by fir filtering we show that such q sub i exist almost surely if and only if m sub q spl ges m sub h 1 p 1 where x is the smallest integer greater than or equal to x the results also provide conditions for full rank of certain key matrices arising in the blind multichannel deconvolution problem

boundary value problems for impulsive integro differential equations on unbounded domains in a banach space in this paper the fixed point theory is used to investigate the existence and uniqueness of solutions of two point boundary value problems bvps for second order non linear impulsive integro differential equations on infinite intervals in a banach space

a penalty method for a mixed nonlinear complementarity problem abstract we propose a power penalty method for a mixed nonlinear complementarity problem mncp and show that the solution to the penalty equation converges to that of the mncp exponentially as the penalty parameter approaches infinity provided that the mapping involved in the mncp is both continuous and monotone furthermore a convergence theorem is established when the monotonicity assumption on the mapping is removed to demonstrate the usefulness and the convergence rates of this method we design a non trivial test mncp problem arising in shape preserving bi harmonic interpolation and apply our method to this test problem the numerical results confirm our theoretical findings

perfect blind restoration of images blurred by multiple filters theory and efficient algorithms we address the problem of restoring an image from its noisy convolutions with two or more unknown finite impulse response fir filters we develop theoretical results about the existence and uniqueness of solutions and show that under some generically true assumptions both the filters and the image can be determined exactly in the absence of noise and stably estimated in its presence we present efficient algorithms to estimate the blur functions and their sizes these algorithms are of two types subspace based and likelihood based and are extensions of techniques proposed for the solution of the multichannel blind deconvolution problem in one dimension we present memory and computation efficient techniques to handle the very large matrices arising in the two dimensional 2 d case once the blur functions are determined they are used in a multichannel deconvolution step to reconstruct the unknown image the theoretical and practical implications of edge effects and weakly exciting images are examined finally the algorithms are demonstrated on synthetic and real data

multivariate generalized sampling in shift invariant spaces and its approximation properties abstract nowadays the topic of sampling in a shift invariant space is having a significant impact it avoids most of the problems associated with classical shannon s theory under appropriate hypotheses any multivariate function in a shift invariant space can be recovered from its samples at z d however in many common situations the available data are samples of some convolution operators acting on the function itself this leads to the problem of multivariate generalized sampling in shift invariant spaces this extra information on the functions in the shift invariant space will allow to sample in an appropriate sub lattice of z d in this paper an l 2 r d theory involving the frame theory is exhibited sampling formulas which are frame expansions for the shift invariant space are obtained in the case of overcomplete frame formulas the search of reconstruction functions with prescribed good properties is allowed finally approximation schemes using these generalized sampling formulas are included

unbounded solutions of the singular boundary value problems for second order differential equations on the half line this paper presents some results on the existence of multiple unbounded solutions for the boundary value problems for second order differential equations on half line and on the uniqueness of unbounded solution

blind identification of multichannel fir blurs and perfect image restoration despite its practical importance in image processing and computer vision blind blur identification and blind image restoration have so far been addressed under restrictive assumptions such as all pole stationary image models blurred by zero or minimum phase point spread functions relying upon diversity availability of a sufficient number of multiple blurred images we develop blind fir blur identification and order determination schemes apart from a minimal persistence of the excitation condition also present with nonblind setups the inaccessible input image is allowed to be deterministic or random and of unknown color of distribution with the blurs satisfying a certain co primeness condition in addition we establish existence and uniqueness results which guarantee that single input multiple output fir blurred images can be restored blindly though perfectly in the absence of noise using linear fir filters results of simulations employing the blind order determination blind blur identification and blind image restoration algorithms are presented when the snr is high direct image restoration is found to yield better results than indirect image restoration which employs the estimated blurs in low snr indirect image restoration performs well while the direct restoration results vary with the delay but improve with larger equalizer orders

numerical solution of linear and nonlinear black scholes option pricing equations this paper deals with the numerical solution of black scholes option pricing partial differential equations by means of semidiscretization technique for the linear case a fourth order discretization with respect to the underlying asset variable allows a highly accurate approximation of the solution for the nonlinear case of interest modeling option pricing with transaction costs semidiscretization technique provides a competitive numerical solution with respect to others recently given in b during m fournier a jungel convergence of a high order compact finite difference scheme for a nonlinear black scholes equation esaim math modelling numer anal modelisation mathematique et analyse numerique 38 2004 359 369 b during black scholes type equations mathematical analysis parameter identification numerical solution dissertation university mainz july 2005

evam an eigenvector based algorithm for multichannel blind deconvolution of input colored signals a new algorithm is proposed for the deconvolution of an unknown possibly colored gaussian or nonstationary signal that is observed through two or more unknown channels described by rational system transfer functions more specifically not only the root pole and zero locations but also the orders of the channel transfer functions are unknown it is assumed that the channel orders may be overestimated the proposed algorithm estimates the orders and root locations of the channel transfer functions therefore it can also be used in multichannel system identification problems the input signal is allowed to be nonstationary and the channel transfer functions may be a nonminimum phase as well as noncausal hence the proposed algorithm is particularly suitable for applications such as dereverberation of speech signals recorded through multiple microphones several experimental results indicate improvement compared to the existing methods in the literature

multiple positive solutions of nonlinear two point boundary value problems we improve the results obtained by erbe hu and wang in a recent paper we show that there exist at least two positive solutions of two point boundary value problems under conditions weaker than those used by erbe hu and wang

multidimensional systems with finite support behaviors signal structure generation and detection the main features of finite multidimensional behaviors are introduced as properties of the trajectories supports and connected with the polynomial matrices adopted for their description observability and local detectability are shown to be equivalent to the kernel representation of a behavior via some parity check matrix ht the main properties of locally undetectable behaviors as well as their connections with the notion of constrained variables are investigated and a general representation result for finite support behaviors is derived the input output representation via generator matrices is finally discussed and some connections between matrix primeness and the constraints every trajectory imposes on the support of the corresponding input are analyzed

quadratic convergence for valuing american options using a penalty method the convergence of a penalty method for solving the discrete regularized american option valuation problem is studied sufficient conditions are derived which both guarantee convergence of the nonlinear penalty iteration and ensure that the iterates converge monotonically to the solution these conditions also ensure that the solution of the penalty problem is an approximate solution to the discrete linear complementarity problem the efficiency and quality of solutions obtained using the implicit penalty method are compared with those produced with the commonly used technique of handling the american constraint explicitly convergence rates are studied as the timestep and mesh size tend to zero it is observed that an implicit treatment of the american constraint does not converge quadratically as the timestep is reduced if constant timesteps are used a timestep selector is suggested which restores quadratic convergence