Stability of numerical methods for jump diffusions and Markovian switching jump diffusions

Stability of numerical methods for jump diffusions and Markovian switching jump diffusions

This work is devoted to stability analysis of numerical solutions for jump diffusions and jump diffusions with Markovian switching. Different from the existing treatment of Euler-Maurayama methods for solutions of stochastic differential equations, we use techniques from stochastic approximation. We analyze the almost sure exponential stability and exponential pstability. Then Markovian regime-...

Numerical methods for controlled regime-switching diffusions and regime-switching jump diffusions

This work is concerned with numerical methods for controlled regime-switching diffusions, and regime-switching jump diffusions. Numerical procedures based on Markov chain approximation techniques are developed. Convergence of the algorithms is derived by means of weak convergence methods. In addition, examples are also provided for demonstration purpose. 2006 Elsevier Ltd. All rights reserved.

First Passage Time Moments of Jump-Diffusions with Markovian Switching

Numerical solutions for jump-diffusions with regime switching

This paper is devoted to numerical solutions for a class of jump-diffusions with regime switching. After briefly reviewing the notion of jump-diffusions with regime switching, finite-difference procedures are constructed. Under simple conditions, it is proved that the algorithm converges to the desired limit by means of a martingale problem formulation. Numerical experiments are carried out to ...

Estimating functions for jump-diffusions

The theory of approximate martingale estimating functions for continuous diffusions is well developed and encompasses many estimators proposed in the literature. This paper extends the asymptotic theory for approximate martingale estimating functions to diffusions with finite-activity jumps. The primary aim is to shed light on the question of rate optimality and efficiency of estimators when ob...