On Explicit Tamed Milstein-type scheme for Stochastic Differential\n Equation with Markovian Switching

2019/09/17 by Chaman Kumar, Kumar, Chaman, Tejinder Kumar +1 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Numerical Analysis (math.NA) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1909.07886

openalex publication_date 2019/09/17 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We propose a new tamed Milstein-type scheme for stochastic differential\nequation with Markovian switching when drift coefficient is assumed to grow\nsuper-linearly. The strong rate of convergence is shown to be equal to 1.0\nunder mild regularity (e.g. once differentiability) requirements on drift and\ndiffusion coefficients. Novel techniques are developed to tackle two-fold\ndifficulties arising due to jumps of the Markov chain and the reduction of\nregularity requirements on the coefficients.\n

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