Optimal portfolio management when stocks are driven by Mean-Reverting Processes
A dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science (Mathematical Modelling) of the University of Dar es Salaam
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| Формат: | Диссертация |
| Язык: | английский |
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University of Dar es Salaam
2024
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| Online-ссылка: | https://scholar.mzumbe.ac.tz/handle/123456789/513 |
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| _version_ | 1835205599515639808 |
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| author | Mbigili, Lusungu Julius |
| author_facet | Mbigili, Lusungu Julius |
| author_sort | Mbigili, Lusungu Julius |
| collection | DSpace |
| description | A dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science (Mathematical Modelling) of the University of Dar es Salaam |
| format | Thesis |
| id | oai:null:123456789-513 |
| institution | Mzumbe University |
| language | English |
| publishDate | 2024 |
| publisher | University of Dar es Salaam |
| record_format | dspace |
| spelling | oai:null:123456789-5132024-03-27T10:19:21Z Optimal portfolio management when stocks are driven by Mean-Reverting Processes Mbigili, Lusungu Julius Ito-diffusion and Generator Bellman's Principle stochastic optimal control A dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science (Mathematical Modelling) of the University of Dar es Salaam In this work, we present and solve the problem of portfolio optimization within the context of continuous-time stochastic model of financial variables. We consider an investment problem where an investor has two assets, namely, risk-free assets (e.g. bonds) and risky assets (e.g. stocks) to invest on and tries to maximize the expected utility of the wealth at some future time. The evolution of the risk-free asset is described deterministically while the dynamics of the risky asset is described by the geometric mean reversion (GMR) model. The controlled wealth stochastic deferential equation (SDE) and the portfolio problem are formulated. The portfolio optimization problem is then successfully formulated and solved with the help of the theory of stochastic control technique where the dynamic programming principle (DPP) and the HJB theory were used. We obtained very interesting results which are the solution of the non-linear second order partial deferential equation and the optimal policy which is the optimal control strategy for the investment process. So far we have considered utility functions which are members of hyperbolic absolute risk aversion (HARA) family, called power and exponential utility. In both cases, the optimal control (investment strategy) has explicit form and is wealth dependent, in the sense that, as the investor becomes more rich, the less he invests on the risky assets. Linearization of the logarithmic term in the portfolio problem was necessary to be undertaken for making the work of obtaining the explicit form of the optimal control much simple than it was expected. Ardhi university 2024-03-27T10:19:17Z 2024-03-27T10:19:17Z 2012 Thesis APA https://scholar.mzumbe.ac.tz/handle/123456789/513 en application/pdf University of Dar es Salaam |
| spellingShingle | Ito-diffusion and Generator Bellman's Principle stochastic optimal control Mbigili, Lusungu Julius Optimal portfolio management when stocks are driven by Mean-Reverting Processes |
| title | Optimal portfolio management when stocks are driven by Mean-Reverting Processes |
| title_full | Optimal portfolio management when stocks are driven by Mean-Reverting Processes |
| title_fullStr | Optimal portfolio management when stocks are driven by Mean-Reverting Processes |
| title_full_unstemmed | Optimal portfolio management when stocks are driven by Mean-Reverting Processes |
| title_short | Optimal portfolio management when stocks are driven by Mean-Reverting Processes |
| title_sort | optimal portfolio management when stocks are driven by mean reverting processes |
| topic | Ito-diffusion and Generator Bellman's Principle stochastic optimal control |
| url | https://scholar.mzumbe.ac.tz/handle/123456789/513 |
| work_keys_str_mv | AT mbigililusungujulius optimalportfoliomanagementwhenstocksaredrivenbymeanrevertingprocesses |