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Advances in Mathematical Finance and Optimal Transport

Controlled measure valued martingales: a viscosity solution approach

speaker: Sigrid Källblad (KTH Royal Institute of Technology Stockholm)

abstract: We consider a class of stochastic control problems where the state process is a probability measure-valued process satisfying an additional martingale condition on its dynamics, called measure-valued martingales (MVMs). We establish the ‘classical’ results of stochastic control for these problems: specifically, we show that the value function for the problem can be characterised as the unique solution to a Hamilton-Jacobi-Bellman equation in the sense of viscosity solutions. In order to obtain this, we exploit structural properties of the MVM processes; in particular, our results include existence of controlled MVMs and an appropriate version of Itô’s formula for such processes. We also illustrate how problems of this type arise in a number of applications including model-independent derivatives pricing. The talk is based on joint work with Alex Cox, Martin Larsson and Sara Svaluto-Ferro.

Thu 30 Jun, 9:15 - 10:00, Aula Dini
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