Markov decision models for dynamic risk management

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The proposed research mainly focuses on a new method for solving nonlinear multiperiod Markov decision models in a setting of dynamic risk management. It involves a design process for highly sophisticated dynamic models applicable to risk management activities. This process can be naturally divided into three steps.First, theoretical models for state variables will be established based on the structure of the system and the control objectives and constraints. The proposed model takes  a set of state indicators as primary sources of risk and characterizes the state dynamics with Markov processes.Second, up-to-date databases will be acquired and used for the estimation of model parameters and validation of the model itself. Highly efficient statistical and simulation algorithms, such as the adapted Expectation and Maximization algorithm, are applied in the estimation procedures.Third, Markov decision models will be formulated and solved to obtain the optimal decision rules and their practical implications. Using a popular risk management measure, such as Value at Risk and Conditional Value at Risk, as the objective function of minimizing risk, the optimal policy is obtained through large-scale stochastic dynamic programming techniques. A novelty of this research is the  decomposition solution technique for multiperiod nonlinear stochastic programming models.The intention of the research program is to build  realistic models for dynamic control under uncertainty and to study efficient solution algorithms for theoretically intractable problems.