2013/09/17 by Plamen Turkedjiev, Turkedjiev, Plamen
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #60H07 #60H10 #60H35 #65C30 #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1309.4378
openalex publication_date 2013/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two discretizations of a class of locally Lipschitz Markovian backward stochastic differential equations (BSDEs) are studied. The first is the classical Euler scheme which approximates a projection of the processes Z, and the second a novel scheme based on Malliavin weights which approximates the mariginals of the process Z directly. Extending the representation theorem of Ma and Zhang leads to advanced a priori estimates and stability results for this class of BSDEs. These estimates are then used to obtain competitive convergence rates for both schemes with respect to the number of points in the time-grid. The class of BSDEs considered includes Lipschitz BSDEs with fractionally smooth terminal condition as well as quadratic BSDEs with bounded, Hölder continuous terminal condition (for bounded, differentiable volatility), and BSDEs related to proxy methods in numerical analysis.