New approach to optimal control of stochastic Volterra integral equations

We study optimal control of stochastic Volterra integral equations (SVIE) with jumps by using Hida-Malliavin calculus. - We give conditions under which there exists unique solutions of such equations. - Then we prove both a sufficient maximum principle (a verification theorem) and a necessary maximum principle via Hida-Malliavin calculus. - As an application we solve a problem of optimal consumption from a cash flow modelled by an SVIE

Malliavin calculus and optimal control of stochastic Volterra equations

Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore classical methods, like dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that by using {\em Malliavin calculus} it is possible to formulate a modified functional type of {\em maximum principle} suitable for such systems. This principle also applies to situations where the controller has only partial information available to base her decisions upon. We present both a sufficient and a necessary maximum principle of this type, and then we use the results to study some specific examples. In particular, we solve an optimal portfolio problem in a financial market model with memory.Comment: 18 page

A white noise approach to insider trading

We present a new approach to the optimal portfolio problem for an insider with logarithmic utility. Our method is based on white noise theory, stochastic forward integrals, Hida-Malliavin calculus and the Donsker delta function.Comment: arXiv admin note: text overlap with arXiv:1504.0258

Stochastic differential games with inside information

We study stochastic differential games of jump diffusions, where the players have access to inside information. Our approach is based on anticipative stochastic calculus, white noise, Hida-Malliavin calculus, forward integrals and the Donsker delta functional. We obtain a characterization of Nash equilibria of such games in terms of the corresponding Hamiltonians. This is used to study applications to insider games in finance, specifically optimal insider consumption and optimal insider portfolio under model uncertainty.Comment: arXiv admin note: text overlap with arXiv:1504.0258

Stochastic Volterra equations with time-changed L\'evy noise and maximum principles

We study an optimal control problem for Volterra type dynamics driven by time-changed L\'evy noises, which are in general not Markovian. To exploit the nature of the noise, we make use of different kind of information flows within a maximum principle approach. For this we work with backward stochastic differential equations (BSDE) with time-change and exploit the non-anticipating stochastic derivative as introduced in [7]. We prove both a stochastic sufficient and necessary maximum principle and we complete the work providing applications to optimal portfolio problems