(YIP) Dynamic Decision Making Under Uncertainty and Partial Information

The researchers made significant progress in all of the proposed research areas. The first major task in the proposal involved duality in stochastic control and optimal stopping. In support of this task, the researchers developed new methods for efficiently solving optimal stopping problems of partially observable Markov processes and optimal stopping problems under jump-diffusion processes. The researchers also studied and established duality for controlled Markov diffusions via the information relaxation approach. In the second major task aiming at solving difficult global optimization problems, the researchers proposed and developed a new framework that integrates the idea of model-based randomized optimization with gradient-based optimization. All the developed methods have been tested through numerical experiments and demonstrated excellent performance. The methods have also been applied to problems in revenue management, option pricing, and power allocation in communication networks.