Mean variance optimalizace pro minimální entropickou míru
| Thesis title in Czech: | Mean variance optimalizace pro minimální entropickou míru |
|---|---|
| Thesis title in English: | Mean Variance Optimization for Minimal Entropy Measure |
| Key words: | Mean variance optimalizace|minimální entropická míra |
| English key words: | Mean variance optimization|minimal entropy measure |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | diploma thesis |
| Thesis language: | čeština |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. RNDr. Jan Večeř, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 04.10.2023 |
| Date of assignment: | 30.10.2023 |
| Confirmed by Study dept. on: | 30.10.2023 |
| Date and time of defence: | 10.06.2024 08:30 |
| Date of electronic submission: | 01.05.2024 |
| Date of submission of printed version: | 01.05.2024 |
| Date of proceeded defence: | 10.06.2024 |
| Opponents: | Mgr. Ing. Pavel Kříž, Ph.D. |
| Guidelines |
| This thesis should address the problem of portfolio optimization in incomplete markets assuming that the market agent has a specific opinion about the physical state price density. In this situation, the agent should find a portfolio with a state price density that is closest in terms of the relative entropy to the agent's density. More specifically, the task should consider the model with normal log returns with two primary assets, a fixed time horizon T, and the agent's opinion that is also normal, but with a different mean and variance. As a static replication of the agent's opinion by the two basic assets is not expected to work well, the model of the market should add one or two European options with different strikes to find a closer fit to the agent's opinion. Moreover, the approach should adopt mean variance approximation to the minimization of the relative entropy in order to find a suitable analytical proxy to the exact solution that is unlikely to have an analytical solution. |
| References |
| Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7, 77-91.
Frittelli, M. (2000). The minimal entropy martingale measure and the valuation problem in incomplete markets. Mathematical finance, 10(1), 39-52. Vecer, J. (2024). Principles of Bayesian Portfolio Selection, CRC Press. |