CEU Electronic Theses and Dissertations, 2016
| Author | Tikosi, Kinga |
|---|---|
| Title | Merton's Portfolio Problem |
| Summary | Merton’s optimal investment problem is a well known problem of continuous time finance, which was named after Nobel laureate Robert Merton’s pioneering work in this area. It concerns finding the optimal investment strategy for the investor, who has only two possible objects of investment: a risk-less asset (e. g. a savings account), paying a fixed rate of interest and a number of risky assets (e. g. stock, real estate) whose price is assumed to follow a geometric Brownian motion. Assume that the investor lives for a finite period of time, from present until time T, he starts with an initial amount of money, and he wants to decide how much of which security to hold at each time in order to maximize the final wealth. Naturally, the investor is risk averse to a certain degree, which means that he refrains from investing in assets which have a high risk of loosing money even if it might have high return. The investor’s attitude to risk and individual preferences can be characterized by the so called utility functions, this way we do not maximize the expected return of the investment, but the expected utility, making it possible not only to maximize the expected value of the final wealth, but also limit the risk of losing money at the same time. The aim of present thesis to develop better understanding of the above presented problem. |
| Supervisor | Rásonyi, Miklós |
| Department | Mathematics MSc |
| Full text | https://www.etd.ceu.edu/2016/tikosi_kinga.pdf |
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