An M-ary detection approach for asset allocation

We develop a continuous-time asset allocation model which incorporates both model uncertainty and structural changes in economic conditions. A "dynamic" M-ary detection framework for a continuous-time hidden Markov chain partially observed in a Gaussian process is used to model the price dynamics of the risky asset and the hidden states of an economy. The goal of an investor is to select an optimal asset portfolio mix so as to maximize the expected utility of terminal wealth. Filtering theory is used first to turn the problem into one with complete observations and then to derive M-ary detection filters for the hidden system. The HamiltonJacobiBellman dynamic programming approach is used to solve the asset allocation problem with complete observations. An explicit solution is obtained for the power utility case.