TitleRisk-averse control of undiscounted transient Markov models
NameCavus, Ozlem (author), BEN-ISRAEL, ADI (chair), Ruszczynski, Andrzej (internal member), Boros, Endre (internal member), Alizadeh, Farid (internal member), Katehakis, Michael N. (outside member), Dentcheva, Darinka (outside member), Rutgers University, Graduate School - New Brunswick,
DescriptionThe classical optimal control problems for discrete-time, transient Markov processes are infinite horizon, undiscounted expected total cost or reward models. Some examples of these models are optimal stopping problems and stochastic shortest or longest path problems, which may have applications in health-care, finance, and maintenance. However, such expected value models implicitly assume the decision maker is risk-neutral, so they may not be appropriate for several real-life problems. In this study, we use Markov risk measures to formulate a risk-averse version of the optimal control problem for transient Markov processes with general state and compact control spaces. We derive risk-averse dynamic programming equations and show that they have a unique solution which is also the optimal value of the Markov control problem. Furthermore, it is shown that a randomized policy may be strictly better than deterministic policies, when risk measures are employed. We suggest two algorithms, value iteration and policy iteration methods, for solving the dynamic programming equations and show their convergence. In general, each policy evaluation step of the policy iteration algorithm requires solving a system of nonsmooth equations. We use a version of nonsmooth Newton method to solve these equations and show its global convergence. We further consider a risk-averse finite horizon Markov control problem under randomized policies and derive a value iteration method for its solution. Finally, we work on asset selling, organ transplant, and credit card examples to illustrate the theory for infinite horizon problem, and present numerical results.
NoteIncludes bibliographical references
Noteby Ozlem Cavus
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.