Many Stochastic Differential Equations (SDEs) that arise in mathematical biology, finance etc. preserve positivity (eg concentrations should be positive) or solutions should lie in a certain domain (eg [0,1]). The question then arises how to preserve these domains in a numerical simulation.
In this talk, we introduce time integrators for semi-linear SDEs based on variation of constant formula and taking advantage of exact formulation of Geometric Brownian Motion (GBM). Then,
a numerical algorithm preserving domain is developed by freezing coefficients of the underlying SDE and applying GBM based integrator.
We discuss convergence and efficieny of the proposed scheme by illustrating numerical test examples. This work is joint with Gabriel Lord.
Back to the seminar page