Nacira Agram: A Hida-Malliavin white noise calculus approach to optimal control
Nacira Agram (University of Oslo) gives a lecture with the title: A Hida-Malliavin white noise calculus approach to optimal control
The classical maximum principle for optimal stochastic control states that if a control u^ is optimal, then the corresponding Hamiltonian has a maximum at u=u^. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently it was discovered by Shige Peng that one could also allow the diffusion coefficient to depend on the control, if the corresponding adjoint BSDE for the first order derivative was extended to include an extra BSDE of second order derivatives.
In this talk we present an alternative approach based on Hida-Malliavin calculus and white noise theory. This enables us to handle the general case with jumps, allowing both the diffusion coefficient and the jump coefficient to depend on the control, and we do not need the extra BSDE with second order derivatives.
The talk is based on recent joint work with Bernt Øksendal.