The Bismut-Elworthy-Li formula for mean-field stochastic differential\n equations

2015/10/23 by David Baños, Baños, David R.
Economics, Econometrics and Finance · Mathematics · #60H07 #60H10 #60J60 #65C05 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistical Distribution Estimation and Applications #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1510.06961

openalex publication_date 2015/10/23 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We generalise the so-called Bismut-Elworthy-Li formula to a class of\nstochastic differential equations whose coefficients might depend on the law of\nthe solution. We give some examples of where this formula can be applied to in\nthe context of finance and the computation of Greeks and provide with a simple\nbut rather illustrative simulation experiment showing that the use of the\nBismut-Elworthy-Li formula, also known as Malliavin method, is more efficient\ncompared to the finite difference method.\n

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