Optimal insider control of stochastic partial differential equations

Abstract

MSC(2010): 60H10, 91A15, 91A23, 91B38, 91B55, 91B70, 93E20 AbstractWe study the problem of optimal inside control of a stochastic Volterra equation driven by a Brownian motion and a Poisson random measure. We prove a sufficient and a necessary maximum principle for the optimal control when the trader has only partial information available to her decisions and on the other hand, may have some inside information about the future of the system. The results are applied to the problem of finding the optimal insider portfolio in a financial market where the risky asset price is given by a stochastic Volterra equation. process, where Z is a given F T 0 -measurable random variable for some T 0 > 0 , representing the inside information available to the controller. Note that from (1.1) we get: dX(t) = ξ ′ (t)dt + b(t, t, X(t, Z), u(t, Z))dt + ( t 0