In the present paper, a class of stochastic Runge–Kutta methods containing the second order stochastic Runge–Kutta scheme due to E. Platen for the weak approximation of Itô stochastic differential equation systems with a multi-dimensional Wiener process is considered. Order 1 and order 2...

We consider scalar stochastic differential equations of the formdXt=μ(Xt)dt+σ(Xt)dBt,X0=x0,where B is a standard Brownian motion. Suppose that the coefficients are such that the solution X possesses the (a, b)-invariance property for some interval (a,b)⊂R:Xt∈(a,b) for all t≥0 if...

Rare and randomly occurring events are important features of the economic world. In continuous time they can easily be modeled by Poisson processes. Analyzing optimal behavior in such a setup requires the appropriate version of the change of variables formula and the Hamilton-Jacobi-Bellman...

The present paper is concerned with the optimal control of stochastic differential equations, where uncertainty stems from one or more independent Poisson processes. Optimal behavior in such a setup (e.g., optimal consumption) is usually determined by employing the Hamilton-Jacobi-Bellman...

Rare and randomly occurring events are important features of the economic world. In continuous time they can easily be modeled by Poisson processes. Analyzing optimal behavior in such a setup requires the appropriate version of the change of variables formula and the Hamilton-Jacobi-Bellman...

This paper considers ML estimation of a diffusion process observed discretely. Since the exact loglikelihood is generally not available, it must be approximated. We review the most effcient approaches in the literature, and point to some drawbacks. We propose to approximate the loglikelihood...