Collaborative Research: Successive Risk-Neutral Approximations of Dynamic Risk-Averse Optimization Problems

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The proposed research aims at developing methods for solving stochastic dynamic optimization problems that involve risk-averse preferences. Mathematical models of risk aversion capture entire distributions of random outcomes with increased attention to events of small probability and high consequences. The project will concentrate on multistage stochastic optimization problems and on Markov decision processes incorporating dynamic risk measures and dynamic stochastic ordering constraints. The proposed numerical approach integrates modern theories of risk measures and stochastic orders with decomposition techniques for large-scale optimization problems, methods of nonsmooth optimization, and stochastic control methods. The approach will be based on sequential risk-neutral approximations of risk-averse problems. The approximations will be used to devise primal and dual decomposition methods for multistage problems with dynamic risk measures and dynamic stochastic ordering constraints. Special attention will be paid to Markov decision problems. A theory of Markov risk measures and risk-averse dynamic programming will be developed. Numerical methods for risk-averse dynamic programming will also explore the idea of sequential risk-neutral approximations.The project will provide qualitative advance in areas involving multi-stage decision-making in stochastic systems under high uncertainty and risk. It will provide modeling and algorithmic tools to formalize and solve long-term planning problems in which risk is an important issue and average performance criteria are insufficient. Problems of this nature arise in supply chain management, military planning problems, energy production and distribution, telecommunication, insurance and finance, medicine, and other areas. The project will benefit the graduate education at Rutgers University and Stevens Institute of Technology.