Construction of positivity preserving numerical schemes for multidimensional stochastic differential equations

Abstract

In this note we work on the construction of positive preserving numerical schemes for systems of stochastic differential equations. We use the semi discrete idea that we have proposed before proposing now a numerical scheme that preserves positivity on multidimensional stochastic differential equations converging strongly in the mean square sense to the true solution.

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• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• Convergence, Non-negativity and Stability of a New Milstein Scheme with Applications to Finance