| Lecturer: | H. Pham |
| Period: | Term 2 |
| ECTS | 6 |
| Schedule: | 3h per week + tutorials |
Registration, access link and informations about this course at:
https://moodle.u-paris.fr/course/view.php?id=6165
Programme:
Stochastic control is a classical topic in applied mathematics and occurs in many practical situations when we have to take decisions under uncertainty. It has known important developments over the last years inspired especially by problems in mathematical finance. To mention some applications: - hedging and pricing of options, - portfolio selection, - risk management, - real options and investment on energy markets, - optimal selling of asset, high frequency trading. The aim of these lectures is to give an overview of the main methods and results in this area.
We first present the standard approach by dynamic programming equation and verification, and point out the limits of this method. We then move on to the viscosity solutions approach: it requires more theory and technique, but provides the general mathematical tool for dealing with stochastic control in a Markovian context. Next, we focus on another important class of stochastic control, namely optimal stopping, which arises typically in American option valuation. The last part will be devoted to the martingale approach for portfolio optimization. The various methods presented in these lectures will be illustrated by several applications arising in economics and finance.
References:
- FLEMING W. & M. SONER (1993), Controlled Markov Processes and Viscosity Solutions, Springer Verlag, 2nd edition 2006.
- PHAM H (2009): Continuous time stochastic control and optimization with financial applications, Springer.
