A transformed jump-adapted backward Euler method for jump-extended CIR and CEV models
type: Item
instance of: scholarly article
title: A transformed jump-adapted backward Euler method for jump-extended CIR and CEV models
zbMATH Open document ID: 1359.65016
author: Xu Yang
author: Xiaojie Wang
published in: Numerical Algorithms
publication date: 2017-01-12T00:00:00Z
review text: A jump-adapted backward Euler method is devised for approximating the solution of a jump-diffusion Itô stochastic differential equation of the form \[ dX_t= \kappa(\theta- X_{t-})\,dt+ \sigma X^\alpha_{t-}dW_t+ g(X_{t-})\,dN_t,\quad t\in(0,T],\quad X(0)= X_0, \] where \(W_t\) is a scalar Wiener process and \(N_t\) is a scalar Poisson process. Such equations arise in mathematical finance. Under certain assumptions, it is proved that positivity will be retained and that the method is strongly convergent with order one in the \(p\)th mean. Numerical results for examples are presented in which a strong convergence rate of order one is attained and positivity is preserved.
reviewed by: Melvin D. Lax
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 6674009
zbMATH Keywords: jump-extended CIR and CEV models
zbMATH Keywords: jump-adapted method
zbMATH Keywords: strong convergence rates
zbMATH Keywords: non-Lipschitz coefficients
zbMATH Keywords: backward Euler method
zbMATH Keywords: jump-diffusion Itô stochastic differential equation
zbMATH Keywords: Wiener process
zbMATH Keywords: Poisson process
zbMATH Keywords: mathematical finance
zbMATH Keywords: numerical results
MaRDI profile type: Publication
full work available at URL: s11075-016-0137-4
OpenAlex ID: W2492225378
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DOI: 10.1007/S11075-016-0137-4
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description: scientific article; zbMATH DE number 6674009