When simulating discrete time approximations of solutions of stochastic differential equations (SDEs), numerical stability is clearly more important than numerical efficiency or some higher order of convergence. Discrete time approximations of solutions of SDEs are widely used in simulations in...

The paper estimates the speed of convergence of the Euler approximation for diffussion processes with jump component which have Holder continuous coefficients.

The purpose of this paper is to study the efficiency of simplified weak schemes for stochastic differential equations. We present a numerical comparison between weak Taylor schemes and their simplified versions. In the simplified schemes discrete random variables, instead of Gaussian ones, are...

A number of inverse problems may be viewed in terms of the approximation of a target element x in a complete metric space (X,d) by the fixed point x* of a contraction function T : X - X. In practice, from a family of contraction functions T(a) one wishes to find the parameter a for which the...

We consider a pension plan with the option of early retirement, and paid benefits $\Psi (S,t)$ based on salary S at the time of retirement, but with guaranteed minimum; $S=S(t)$ is a Markov process. Denote by V(S,t) the financial value of the retirement benefits; its formal definition is given...

This paper introduces a new class of numerical schemes for the pathwise approximation of solutions of stochastic differential equations (SDEs). The proposed family of strong predictor-corrector Euler methods are designed to handle scenario simulation of solutions of SDEs. It has the potential to...

The paper studies the application of the balanced method in hidden Markov chain filtering, an important practical area that requires the strong numerical solution of stochstic differential equations with multiplicative noise. Numerical experiments are conducted to enable comparisons between the...