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Boundary Preserving Semianalytic Numerical Algorithms for Stochastic Differential Equations

Construction of splitting-step methods and properties of related nonnegativity and boundary preserving semianalytic numerical algorithms for solving stochastic differential equations (SDEs) of Ito type are discussed. As the crucial assumption, we oppose conditions such that one can decompose the original system of SDEs into subsystems for which one knows either the exact solution or its conditional transition probability. We present convergence proofs for a newly designed splitting-step algorithm and simulation studies for numerous well-known numerical examples ranging from stochastic dynamics occurring in asset pricing in mathematical finance (Cox-Ingersoll-Ross (CIR) and constant elasticity of variance (CEV) models) to measure-valued diffusion and super-Brownian motion (stochastic PDEs (SPDEs)) as met in biology and physics.