a numerical method for pricing discrete double barrier option by legendre multiwavelet in this article a fast numerical algorithm for pricing discrete double barrier option is presented according to blackscholes model the price of option in each monitoring date can be evaluated by a recursive formula upon the heat equation solution these recursive solutions are approximated by using legendre multiwavelets as orthonormal basis functions and expressed in operational matrix form the most important feature of this method is that its cpu time is nearly invariant when monitoring dates increase besides the rate of convergence of presented algorithm was obtained the numerical results verify the validity and efficiency of the numerical method

existence of coupled quasi solutions of systems of nonlinear reaction diffusion equations systems of nonlinear parabolic initial boundary value problems arise in many applications such as epidemies ecology biochemistry biology chemical and nuclear engineering constructive methods of proving existence results for such problems which can also provide numerical procedures for the computation of solutions are of greater value than theoretical existence results the method of upper and lower solutions coupled with monotone iterative technique has been employed successfully to prove existence of multiple solutions of nonlinear reaction diffusion equations in special cases by various authors 335 10 11 15 181 recently in 6 171 weakly coupled systems of reaction diffusion equations when the nonlinear terms are independent of gradient terms are discussed and some special type of results are obtained we in this paper investigate general systems of nonlinear reaction diffusion problems when the nonlinear terms possess a mixed quasi monotone property we discuss a very general situation and obtain coupled extremal quasi solutions which in special cases reduce to minimal and maximal solutions we shall also indicate how one step cyclic monotone iterative schemes can be generated which yield accelerated rate of convergence of iterates this work is in the spirit of our recent paper 12 for elliptic systems

laplace transform inversion on the real line is truly ill conditioned in this note we consider laplace transforms of probability distribution functions f t on 0 that have finite integer moments of all orders we construct a family f w t of distribution functions whose laplace transforms differ from that of f t by as little as we want but such that f w t has a discrete part whereas f t has a density f t thus we provide one more example of why laplace transform inversion on the real line is a difficult ill conditioned inverse problem

laplace transform and finite difference methods for the black scholes equation in this paper we explore discrete monitored barrier options in the black scholes framework the discontinuity arising at each monitoring data requires a careful numerical method to avoid spurious oscillations when low volatility is assumed here a technique mixing the laplace transform and the finite difference method to solve black scholes pde is considered equivalence between the post widder inversion formula joint with finite difference and the standard finite difference technique is proved the mixed method is positivity preserving satisfies the discrete maximum principle according to financial meaning of the involved pde and converges to the underlying solution in presence of low volatility equivalence between methods allows some physical interpretations

frechet differentiability for a damped sine gordon equation abstract we consider a damped sine gordon equation with a variable diffusion coefficient the goal is to derive necessary conditions for the optimal set of parameters minimizing the objective function j first we show that the solution map is continuous under a weak assumption on the topology of the admissible set p then the solution map is shown to be weakly g teux differentiable on p implying the g teux differentiability of the objective function finally we show the frechet differentiability of j the optimal set of parameters is shown to satisfy a bang bang control law

on convergence of the modified newton s method under holder continuous frechet derivative in this paper the upper and lower estimates of the radius of the convergence ball of the modified newton s method in banach space are provided under the hypotheses that the frechet derivative of the nonlinear operator are center holder continuous for the initial point and the solution of the operator the error analysis is given which matches the convergence order of the modified newton s method the uniqueness ball of solution is also established numerical examples for validating the results are also provided including a two point boundary value problem

global wave front sets of banach frechet and modulation spacetypes and pseudo differential operators we introduce global wave front sets with respect to suitable banach or frechet spaces an important special case appears when choosing these spaces as modulation spaces we show that the standard p

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

option pricing for a large trader with price impact and liquidity costs abstract this paper concerns the pricing of options for a large trader in a market with liquidity risk the investor s trading action is assumed to have some lasting impact on the underlying asset and the effect of illiquidity is modeled via trading speed rate of change in holdings for such a large trader liquidity risk is quite important since the permanent price impact as well as liquidity costs incurred during trading must be taken into account the utility maximization approach to determine option prices leads to optimal control problems this paper shows that the value functions of these optimal control problems are the unique viscosity solutions of a fully nonlinear second order pde moreover some illustrative examples with explicit optimal solutions and numerical results are presented

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

robust numerical algorithm to the european option with illiquid markets abstract in this paper we consider illiquid european call option which is arisen in nonlinear black scholes equation in this respect we apply the newton s method to linearize it based on the obtained linear equation we obtain the approximate solutions recursively in two steps finally based on the conditions of kantorovich theorem we investigate the convergence analysis of the newton s method on the proposed problem finally the positivity of the solution is discussed

on nonlinear reaction diffusion systems abstract this paper presents a qualitative analysis for a coupled system of two reaction diffusion equations under various boundary conditions which arises from a number of physical problems the nonlinear reaction functions are classified into three basic types according to their relative quasi monotone property for each type of reaction functions an existence comparison theorem in terms of upper and lower solutions is established for the time dependent system as well as some boundary value problems three concrete physical systems arising from epidemics biochemistry and engineering are taken as representatives of the basic types of reacting problems through suitable construction of upper and lower solutions various qualitative properties of the solution for each system are obtained these include the existence and bounds of time dependent solutions asymptotic behavior of the solution stability and instability of nontrivial steady state solutions estimates of stability regions and finally the blowing up property of the solution special attention is given to the homogeneous neumann boundary condition

numerical solutions for some coupled systems of nonlinear boundary value problems in the well known volterra lotka model concerning two competing species with diffusion the densities of the species are governed by a coupled system of reaction diffusion equations the aim of this paper is to present an iterative scheme for the steady state solutions of a finite difference system which corresponds to the coupled nonlinear boundary value problems this iterative scheme is based on the method of upper lower solutions which leads to two monotone sequences from some uncoupled linear systems it is shown that each of the two sequences converges to a nontrivial solution of the discrete equations the model under consideration may have one two or three nonzero solutions and each of these solutions can be computed by a suitable choice of initial iteration numerical results are given for these solutions under both the dirichlet boundary condition and the mixed type boundary condition

discrete event systems with stochastic processing times discrete event dynamic systems are studied in which the underlying algebra is the max algebra and the coefficients in the system referring to processing times in practice are stochastic the processing times and or the transportation times within a network show stochastic fluctuations the restrictions are that the stochastic processing times of the nodes in the network are independent and identically distributed the asymptotic behavior of the system is investigated and the average duration of one cycle of the process is calculated a specific example of the theory is considered the state space is two dimensional and the probability distributions are exponential it is shown that the process approaches a stationary limit as time proceeds the case when the probability distributions are discrete is also treated several examples are given two dimensional systems and more generally finite dimensional systems are considered

born expansion and frechet derivatives in nonlinear diffuse optical tomography the nonlinear diffuse optical tomography dot problem involves the inversion of the associated coefficient to measurement operator which maps the spatially varying optical coefficients of turbid medium to the boundary measurements the inversion of the coefficient to measurement operator is approximated by using the frechet derivative of the operator in this work we first analyze the born expansion show the conditions which ensure the existence and convergence of the born expansion and compute the error in the mth order born approximation then we derive the mth order frechet derivatives of the coefficient to measurement operator using the relationship between the frechet derivatives and the born expansion

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

coexistence and stability of a competition diffusion system in population dynamics abstract the coexistence and stability of the population densities of two competing species in a bounded habitat are investigated in the present paper where the effect of dispersion transportation is taken into consideration the mathematical problem involves a coupled system of lotka volterra type reaction diffusion equations together with some initial and boundary conditions including the dirichlet neumann and third type necessary and sufficient conditions for the coexistence and competitive exclusion are established and the effect of diffusion is explicitly given for the stability problem general criteria for the stability and instability of a steady state solution are established and then applied to various situations depending on the relative magnitude among the physical parameters also given are necessary and sufficient conditions for the existence of multiple steady state solutions and the stability or instability of each of these solutions special attention is given to the neumann boundary condition with respect to which some threshold results for the coexistence and stability or instability of the four uniform steady states are characterized it is shown in this situation that only one of the four constant steady states is asymptotically stable while the remaining three are unstable the stability or instability of these states depends solely on the relative magnitude among the various rate constants and is independent of the diffusion coefficients

on the numerical solution of nonlinear option pricing equation in illiquid markets abstract in this paper we focus on the numerical solution of nonlinear black scholes equation modeling illiquid markets two monotone unconditionally stable splitting methods ensuring positive numerical solution and avoiding unstable oscillations are applied to solve nonlinear black scholes equation modeling illiquid markets these numerical methods are based on the lod methods which allow us to solve the discrete equation explicitly the properties of these methods are analyzed the numerical results for vanilla call option are compared to the local crank nicolson scheme the numerical results for european butterfly spread are also provided