Stokhastik marketlerde portföy seçimi problemine fayda bazlı yaklaşım

In this thesis, we consider the optimal portfolio selection problem in multiple period and continuous time settings where the investor maximizes the expected utility of the terminal wealth in a stochastic market. The utility function has the structure of the HARA family and the market states change according to a Markov chain. The states of the market describe the prevailing economic, financial, social and other conditions that affect the deterministic and probabilistic parameters of the model.In first part we assumed a discrete time market and discuss the stochastic structure of the wealth process under the optimal policy and determine various quantities of interest including its Fourier transform. The exponential, power and logarithmic return-risk frontiers of the terminal wealth is shown to have a linear form.In the second part we investigated the case where the investor does not have perfect information about the market. The unobserved stochastic market is a Markov chain and it emits signals, or provides information, that is observed by the market players. The optimal portfolio policy under imperfect information is constructed and the differences between the perfect and imperfect information cases are presented.In the last part, we analyzed a Black-Scholes type continuous time models where the market parameters are driven by Markov processes. The problem of maximizing the expected utility from terminal wealth is investigated. We found explicit solutions for optimal policy and the associated value functions. We also constructed the optimal wealth process explicitly and discussed some of its properties.