|Organizers||Prof. Martin Schweizer, Danijel Zivoi|
|Place and Time||HG E 1.1, Thursday 13:00 - 15:00|
|First meeting||Thursday 23.02.12|
|Prerequisities||Solid knowledge of continuous stochastic processes is required. Some knowledge in mathematical finance and of PDEs is an advantage but not necessary.|
|Registration||We welcome registrations before the first meeting (send an e-mail to Danijel).|
This seminar is (primarily) aimed at Master's students interested in stochastic calculus, mathematical finance and stochastic control theory. We study selected chapters from Pham's book (see below).
Stochastic control theory is the study of dynamical systems subject to random perturbations which can be controlled in order to optimize some performance criteria. As in classical control theory, there is a fundamental connection between the dynamic programming principle (DPP) associated to a stochastic control problem (for continuous Markov processes) and the so-called Hamilton-Jacobi-Bellman (HJB) equation. We study existence, uniqueness and comparison principles of this (nonlinear parabolic partial differential) equation in an appropriate framework. As an illustration the following concrete examples are discussed:
- Merton's portfolio allocation problem on a finite horizon,
- Investment-consumption problem with random time horizon and
- Superreplication in an uncertain volatility model.
Finally, we study important relations between backward stochastic differential equations (BSDEs) and the HJB equation. Applications are:
- Exponential utility maximization with option payoff and
- Mean-variance criterion for portfolio selection.
Huyên Pham: Continuous-time Stochastic Control and Optimization with Financial Applications
(available on springerlink)
- The seminar will be organised in the style of a reading group. Each student is expected to give a talk of 90 minutes, with a short summary of 1-2 pages to be distributed beforehand.
- The seminar yields 6 credit points. To obtain these, students are expected to (1) regularly attend the seminar, (2) give a successful talk of 90 minutes, (3) provide in advance a PDF summary of their talk of 1-2 pages.
- Depending on the quality of the talk, additional written supplements may be demanded to judge whether (2) is fulfilled.
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