| Some investment and consumption problems with hidden Markov and regime switching structures are studied in this thesis. The financial market consists of a risky asset with random returns and a riskless asset, which generates random returns with a constant expectation, or simply a constant return rate.;The solution of the optimal strategy is characterized for the power utility function. The properties of the optimal strategy and the relevant algorithms are discussed for the case in which the random return rate of the risky asset follows a normal distribution with unknown parameters.;At the beginning of each investment period, a consumption decision is made from the total available wealth and then an investment decision is made on the proportion of the remaining wealth to be invested in the risky asset. The riskless asset return rate is assumed to be random with a constant expectation or simply a constant return rate, but the random return rate of the risky asset depends on the market environment, which is characterized by a discrete-time hidden Markov chain. The Bayesian method is used to model the information gathering process on the risky asset in a finite time horizon model. According to the accumulated information, we estimate the transition probabilities of the Markov process, which characterizes the market environment during the next few investment periods, and then predict the expected return from the risky asset. We also investigate the sensitivity of the optimal solution with respect to the investment horizon and other factors such as the expected return rate from the riskless asset and the consumption rate. Therefore the investor's investment and consumption decision problem is formulated as an optimal stochastic control problem. |
