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

D.J. Higham, G.D. Chalmers

Research output: Contribution to journalArticle

24 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)47-64
Number of pages17
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume9
Issue number1
Publication statusPublished - Jan 2008

Keywords

  • mean-square stability
  • backward Euler
  • diffusion
  • jump
  • strong
  • convergence

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