This paper studies the application of exact simulation methods for multi-dimensional multiplicative noise stochastic differential equations to filtering. Stochastic differential equations with multiplicative noise naturally occur as Zakai equation in hidden Markov chain filtering. The paper...

Simulation estimators, such as indirect inference or simulated maximum likelihood, are successfully employed for estimating models where the likelihood function does not have a simple analytical expression. They adjust for the bias (inconsistency) produced by the estimation of an auxiliary model...

We consider an investor who has available a bank account (risk free asset) and a stock (risky asset). It is assumed that the interest rate for the risk free asset is zero and the stock price is modeled by a diffusion process. The wealth can be transferred between the two assets under a...

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...