Sensitivity Analysis of Expectation with respect to Stochastic Differential Equations with Long Memory through Malliavin Calculus

摘要

Sensitivity formulas of the expectation of stochastic systems, which are written by linear stochas-tic differential equations with long memory, are given through the Malliavin calculus. The fractional Brownian motions are used as noises with long memory. Through the Malliavin method, we do not need to introduce difference approximation parameters like the finite difference method, and numer-ical results do not depend on the parameter values. Numerical results with localization as variance reduction are also given in order to obtain more stable results.