Ergodic risk-sensitive control-A survey

被引：8
作者：
Biswas, Anup [1 ]
Borkar, Vivek S. [2 ]
机构：
[1] Indian Inst Sci Educ & Res Pune, Dept Math, Dr Homi Bhabha Rd, Pune 411008, India
[2] Indian Inst Technol, Dept Elect Engn, Mumbai 400076, India
来源：
ANNUAL REVIEWS IN CONTROL | 2023年 / 55卷
关键词：
Risk-sensitive control; Bellman equation; Generalized principal eigenvalue; Multiplicative dynamic programming; Verification theorem; Markov decision process; MARKOV DECISION-PROCESSES; INFINITE-HORIZON RISK; 2ND-ORDER ELLIPTIC-OPERATORS; VANISHING DISCOUNT APPROACH; FINITE-STATE MACHINES; AVERAGE COST; DISCRETE-TIME; BELLMAN EQUATIONS; PRINCIPAL EIGENVALUE; VARIATIONAL FORMULA;
D O I：
10.1016/j.arcontrol.2023.03.001
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Risk-sensitive control has received considerable interest since the seminal work of Howard and Matheson (Howard and Matheson, 1971/72) because of its ability to account for fluctuations about the mean, its connection with ������& INFIN; control, and its application to financial mathematics. In this article we attempt to put together a comprehensive survey on the research done on ergodic risk-sensitive control over the last four decades.
引用
收藏
页码：118 / 141
页数：24
相关论文
共 157 条
[11]   On the policy improvement algorithm for ergodic risk-sensitive control [J].
Arapostathis, Ari ;
Biswas, Anup ;
Pradhan, Somnath .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2021, 151 (04) :1305-1330
[12]   A VARIATIONAL CHARACTERIZATION OF THE RISK-SENSITIVE AVERAGE REWARD FOR CONTROLLED DIFFUSIONS ON Rd [J].
Arapostathis, Ari ;
Biswas, Anup ;
Borkar, Vivek S. ;
Kumar, K. Suresh .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2020, 58 (06) :3785-3813
[13]   A VARIATIONAL FORMULA FOR RISK-SENSITIVE CONTROL OF DIFFUSIONS IN Rd [J].
Arapostathis, Ari ;
Biswas, Anup .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2020, 58 (01) :85-103
[14]   ERGODIC CONTROL OF A CLASS OF JUMP DIFFUSIONS WITH FINITE LEVY MEASURES AND ROUGH KERNELS [J].
Arapostathis, Ari ;
Caffarelli, Luis ;
Pang, Guodong ;
Zheng, Yi .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2019, 57 (02) :1516-1540
[15]   Strict monotonicity of principal eigenvalues of elliptic operators in Rd and risk-sensitive control [J].
Arapostathis, Ari ;
Biswas, Anup ;
Saha, Subhamay .
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 124 :169-219
[16]   CERTAIN LIOUVILLE PROPERTIES OF EIGENFUNCTIONS OF ELLIPTIC OPERATORS [J].
Arapostathis, Ari ;
Biswas, Anup ;
Ganguly, Debdip .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 371 (06) :4377-4409
[17]   Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions [J].
Arapostathis, Ari ;
Biswas, Anup .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2018, 128 (05) :1485-1524
[18]   Risk-Sensitive Control and an Abstract Collatz-Wielandt Formula [J].
Arapostathis, Ari ;
Borkar, Vivek S. ;
Kumar, K. Suresh .
JOURNAL OF THEORETICAL PROBABILITY, 2016, 29 (04) :1458-1484
[19]  
Arapostathis Ari., 2020, Banach Center Publications, V122, P9
[20]   Optimal dividend payout model with risk sensitive preferences [J].
Baeuerle, Nicole ;
Jaskiewicz, Anna .
INSURANCE MATHEMATICS & ECONOMICS, 2017, 73 :82-93
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