RISK-AVERSE CONTROL OF UNDISCOUNTED TRANSIENT MARKOV MODELS

被引:17
作者
Cavus, Ozlem [1 ]
Ruszczynski, Andrzej [2 ]
机构
[1] Bilkent Univ, Dept Ind Engn, Ankara, Turkey
[2] Rutgers State Univ, Dept Management Sci & Informat Syst, Piscataway, NJ 08854 USA
基金
美国国家科学基金会;
关键词
dynamic risk measures; Markov risk measures; multikernels; stochastic shortest path; optimal stopping; randomized policy; STOCHASTIC-DOMINANCE; DECISION-PROCESSES; ROBUST-CONTROL;
D O I
10.1137/13093902X
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
We use Markov risk measures to formulate a risk-averse version of the undiscounted total cost problem for a transient controlled Markov process. Using the new concept of a multikernel, we derive conditions for a system to be risk transient, that is, to have finite risk over an infinite time horizon. We derive risk-averse dynamic programming equations satisfied by the optimal policy and we describe methods for solving these equations. We illustrate the results on an optimal stopping problem and an organ transplantation problem.
引用
收藏
页码:3935 / 3966
页数:32
相关论文
共 52 条
[1]   The optimal timing of living-donor liver transplantation [J].
Alagoz, O ;
Maillart, LM ;
Schaefer, AJ ;
Roberts, MS .
MANAGEMENT SCIENCE, 2004, 50 (10) :1420-1430
[2]  
[Anonymous], 1998, Variational Analysis
[3]  
[Anonymous], 1969, Markov processes: theorems and problems
[4]  
[Anonymous], 1975, Introduction to Stochastic Processes
[5]   Coherent measures of risk [J].
Artzner, P ;
Delbaen, F ;
Eber, JM ;
Heath, D .
MATHEMATICAL FINANCE, 1999, 9 (03) :203-228
[6]   Coherent multiperiod risk adjusted values and Bellman's principle [J].
Artzner, Philippe ;
Delbaen, Freddy ;
Eber, Jean-Marc ;
Heath, David ;
Ku, Hyejin .
ANNALS OF OPERATIONS RESEARCH, 2007, 152 (1) :5-22
[7]  
Aubin J.P., 1990, SET VALUED ANAL, DOI 10.1007/978-0-8176-4848-0
[8]  
Bäuerle N, 2011, UNIVERSITEXT, P1, DOI 10.1007/978-3-642-18324-9
[9]   AN ANALYSIS OF STOCHASTIC SHORTEST-PATH PROBLEMS [J].
BERTSEKAS, DP ;
TSITSIKLIS, JN .
MATHEMATICS OF OPERATIONS RESEARCH, 1991, 16 (03) :580-595
[10]   Computational Methods for Risk-Averse Undiscounted Transient Markov Models [J].
Cavus, Ozlem ;
Ruszczynski, Andrzej .
OPERATIONS RESEARCH, 2014, 62 (02) :401-417