Malliavin Calculus and Optimal Control of Stochastic Volterra Equations

Malliavin Calculus Applied to Optimal Control of Stochastic Partial Differential Equations with Jumps

In this paper we employ Malliavin calculus to derive a general stochastic maximum principle for stochastic partial differential equations with jumps under partial information. We apply this result to solve an optimal harvesting problem in the presence of partial information. Another application pertains to portfolio optimization under partial observation.

Application of Malliavin calculus to stochastic partial differential equations

The Malliavin calculus is an infinite dimensional calculus on a Gaussian space, which is mainly applied to establish the regularity of the law of nonlinear functionals of the underlying Gaussian process. Suppose that H is a real separable Hilbert space with scalar product denoted by 〈·, ·〉H . The norm of an element h ∈ H will be denoted by ‖h‖H . Consider a Gaussian family of random variables W...

Optimal Control with Partial Information for Stochastic Volterra Equations

In the first part of the paper, we obtain existence and characterizations of an optimal control for a linear quadratic control problem of linear stochastic Volterra equations. In the second part, using the Malliavin calculus approach, we deduce a general maximum principle for optimal control of general stochastic Volterra equations. AMS Subject Classification: Primary 60H15 Secondary 93E20, 35R60.

Optimal Control for Stochastic Volterra Equations with Completely Monotone Kernels

In this paper, we study a class of stochastic optimal control problems, where the drift term of the equation has a linear growth on the control variable, the cost functional has a quadratic growth, and the control process belongs to the class of square integrable, adapted processes with no bound assumed on it. 2000 Mathematics Subject Classification: Primary 45D05 Secondary 93E20, 60H30

Sensitivity analysis using Itô-Malliavin calculus and application to stochastic optimal control