On Approximation of the Backward Stochastic Differential Equation

2013/05/16 by Yury A. Kutoyants, Li Zhou, Kutoyants, Yury A. +1
Economics, Econometrics and Finance · #62M05 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1305.3728

openalex publication_date 2013/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of approximation of the solution of the backward stochastic differential equation in the Markovian case. We suppose that the trend coefficient of the diffusion process depends on some unknown parameter and the diffusion coefficient of this equation is small. We propose an approximation of this solution based on the one-step MLE of the unknown parameter and we show that this approximation is asymptotically efficient in the asymptotics of "small noise".

Related

• Mean square rate of convergence for random walk approximation of forward-backward SDEs
• Approximation analysis for weak solutions of stochastic partial differential equations
• Approximation of BSDE with Hidden Forward Equation and Unknown Volatility
• Stochastic differential equations: loss of the Markov property by multiplicative noise
• Two algorithms for the discrete time approximation of Markovian backward stochastic differential equations under local conditions