| We consider three different problems: (1) optimizing various Metropolis-Hastings algorithms; (2) a hypothesis testing problem under loss of identifiability with a prior distribution on mixing parameter; (3) utility maximization problems of mixed optimal stopping/control for an investor who remains in the stock market until a “retirement” time.; In Chapter I and II we propose an algorithm based on multiple importance sampling techniques to optimize various Metropolis-Hastings kernels by maximizing the expected squared jumped distance. In Chapter III we derive the asymptotic distribution of the likelihood ratio test statistics with a prior distribution on mixing parameter. In Chapter IV, we propose sufficient conditions for the existence of an optimal investment/consumption strategy in the context of Itö's model and derive it explicitly for the case of infinite-horizon with constant coefficients market. |
