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Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes

Higham, D.J. and Chalmers, G.D. (2008) Convergence and stability analysis for implicit simulations of stochastic differential equations with random jump magnitudes. Discrete and Continuous Dynamical Systems - Series B, 9 (1). pp. 47-64. ISSN 1531-3492

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Abstract

Stochastic differential equations with Poisson driven jumps of random magnitude are popular as models in mathematical finance. Strong, or pathwise, simulation of these models is required in various settings and long time stability is desirable to control error growth. Here, we examine strong convergence and mean-square stability of a class of implicit numerical methods, proving both positive and negative results. The analysis is backed up with numerical experiments.

Item type: Article
ID code: 13552
Keywords: mean-square stability, backward Euler, diffusion, jump, strong, convergence, Mathematics, Discrete Mathematics and Combinatorics, Applied Mathematics
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Faculty of Science > Mathematics and Statistics > Mathematics
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Depositing user: Mrs Irene Spencer
Date Deposited: 07 Jan 2010 15:35
Last modified: 04 Sep 2014 22:31
URI: http://strathprints.strath.ac.uk/id/eprint/13552

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