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 journalArticlepeer-review

Abstract / Description of output

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 pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume9
Issue number1
DOIs
Publication statusPublished - Jan 2008

Keywords / Materials (for Non-textual outputs)

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

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