Stochastic algorithmic differentiation of (expectations of) discontinuous functions (indicator functions)

In this paper, we present a method for the accurate estimation of derivative (aka. sensitivity) expectations functions involving an indicator function by modifying (stochastic) algorithmic differentiation, replacing with suitable operator. We show that can split operator into conditional expectation and density. This allows using different or improved numerical approximation methods these operators, e.g. regression. The is improvement approach presented in C.P. Fries [Automatic backward differentiation American Monte-Carlo algorithms (conditional expectation). Risk, April, 2018; Stochastic automatic differentiation: Automatic simulations, Quant. Finance 19(6) (2019), pp. 1043–1059]. finite difference partial integral discontinuous known to exhibit high error. issue evident since just sum as such, not even differentiable. problematic. A natural replace discontinuity continuous functions. equivalent path-wise (local) approximation. decoupling integration Dirac delta remaining introduced here results terms variance reduction implementation design.