Stochastics and Finance Seminar: Max Nendel -- Chernov type approximations of semigroups

Dear Colleagues, at 2PM on Tuesday, February 4, we will have a talk by Prof.  Max
Nendel.  

Title: Chernoff approximation of infinitely divisible distributions and drift
control problems with Levy dynamics 

Abstract: The first part of the talk is concerned with a sufficient condition for
families of probability measures, indexed by positive real numbers, to give rise to a
convolution semigroup via Chernoff approximation on the space of bounded continuous
functions, equipped with the mixed topology.  We provide explicit criteria for both the
convergence of subsequences and the entire family.  In the second part of the talk, we
consider a stochastic version of the Hopf-Lax formula, where the Hopf-Lax operator is
composed with the transition kernel of a Lévy process taking values in a real separable
Banach space.  We show that, depending on the order of the composition, one obtains
upper and lower bounds for the value function of a stochastic optimal control problem
associated to the drift controlled Levy dynamics.  Dynamic consistency is restored by
iterating the resulting operators.  Moreover, the value function of the control problem
is approximated both from above and below as the number of iterations tends to infinity,
and we provide explicit convergence rates for the approximation procedure.