Controlled Measure-Valued Martingales: a Viscosity Solution Approach

Autor:	Cox, Alexander M. G., Källblad, Sigrid, Larsson, Martin, Svaluto-Ferro, Sara
Rok vydání:	2021
Předmět:	Mathematics - Probability Mathematics - Analysis of PDEs Mathematics - Optimization and Control Quantitative Finance - Mathematical Finance Primary: 93E20 49L25 60G57 58J65. Secondary: 60G48 58C20 46T05 91G20 91A27
Druh dokumentu:	Working Paper
Popis:	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 prove that the value function for the problem can be characterised as the unique solution to the Hamilton-Jacobi-Bellman equation in the sense of viscosity solutions. In order to prove this result, we exploit structural properties of the MVM processes. Our results also include an appropriate version of It\^o's lemma for controlled MVMs. We also show how problems of this type arise in a number of applications, including model-independent derivatives pricing, the optimal Skorokhod embedding problem, and two player games with asymmetric information. Comment: 56 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.00064 Zobrazit plný text záznamu View this record from Arxiv