Skip to main content
Top
Published in: Decisions in Economics and Finance 1/2020

15-02-2019

Optimal markov strategies

Author: William D. Sudderth

Published in: Decisions in Economics and Finance | Issue 1/2020

Login to get access

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

For discrete Dubins–Savage gambling problems (Markov decision processes) with payoff equal to the limsup of the utilities of the sequence of successive states, the existence of an optimal strategy at every fortune implies the existence of an optimal Markov strategy at every fortune. If the state space is finite, the same is true when the payoff is the liminf.
Literature
go back to reference Blackwell, D.: Discounted dynamic programming. Ann. Math. Stat. 36, 226–235 (1965)CrossRef Blackwell, D.: Discounted dynamic programming. Ann. Math. Stat. 36, 226–235 (1965)CrossRef
go back to reference Blackwell, D.: On stationary policies. J. R. Stat. Soc. Ser. A 133, 33–37 (1970)CrossRef Blackwell, D.: On stationary policies. J. R. Stat. Soc. Ser. A 133, 33–37 (1970)CrossRef
go back to reference Dubins, L., Savage, L.: How to Gamble If You Must: Inequalities for Stochastic Processes. McGraw-Hill, New York (1965) (Dover editions in 1976 and 2014) Dubins, L., Savage, L.: How to Gamble If You Must: Inequalities for Stochastic Processes. McGraw-Hill, New York (1965) (Dover editions in 1976 and 2014)
go back to reference Flesch, J., Predtetchinski, A., Sudderth, W.: Simplifying optimal strategies in limsup and liminf games. J. Appl. Probab. (2018) (to appear) Flesch, J., Predtetchinski, A., Sudderth, W.: Simplifying optimal strategies in limsup and liminf games. J. Appl. Probab. (2018) (to appear)
go back to reference Hill, T.P.: On the existence of good Markov strategies. Trans. Am. Math. Soc. 247, 157–176 (1979)CrossRef Hill, T.P.: On the existence of good Markov strategies. Trans. Am. Math. Soc. 247, 157–176 (1979)CrossRef
go back to reference Hill, T.P., Pestien, V.C.: The existence of good Markov strategies for decision processes with general payoffs. Stoch. Process. Appl. 24, 61–76 (1987)CrossRef Hill, T.P., Pestien, V.C.: The existence of good Markov strategies for decision processes with general payoffs. Stoch. Process. Appl. 24, 61–76 (1987)CrossRef
go back to reference Maitra, A., Sudderth, W.: Discrete Gambling and Stochastic Games. Springer, New York (1996)CrossRef Maitra, A., Sudderth, W.: Discrete Gambling and Stochastic Games. Springer, New York (1996)CrossRef
go back to reference Orkin, M.: On stationary policies-the general case. Ann. Stat. 2, 219–222 (1974)CrossRef Orkin, M.: On stationary policies-the general case. Ann. Stat. 2, 219–222 (1974)CrossRef
go back to reference Ornstein, D.: On the existence of stationary optimal strategies. Proc. Am. Math. Soc. 20, 563–569 (1969)CrossRef Ornstein, D.: On the existence of stationary optimal strategies. Proc. Am. Math. Soc. 20, 563–569 (1969)CrossRef
go back to reference Strauch, R.: Negative dynamic programming. Ann. Math. Stat. 37, 871–890 (1966)CrossRef Strauch, R.: Negative dynamic programming. Ann. Math. Stat. 37, 871–890 (1966)CrossRef
go back to reference Strauch, R.: Measurable gambling houses. Trans. Am. Math. Soc. 126, 64–72 (1967)CrossRef Strauch, R.: Measurable gambling houses. Trans. Am. Math. Soc. 126, 64–72 (1967)CrossRef
go back to reference Sudderth, W.: Gambling problems with a limit inferior payoff. Math. Oper. Res. 8, 287–297 (1983)CrossRef Sudderth, W.: Gambling problems with a limit inferior payoff. Math. Oper. Res. 8, 287–297 (1983)CrossRef
go back to reference Sudderth, W.: Finitely additive dynamic programming. Math. Oper. Res. 41, 92–108 (2016)CrossRef Sudderth, W.: Finitely additive dynamic programming. Math. Oper. Res. 41, 92–108 (2016)CrossRef
Metadata
Title
Optimal markov strategies
Author
William D. Sudderth
Publication date
15-02-2019
Publisher
Springer International Publishing
Published in
Decisions in Economics and Finance / Issue 1/2020
Print ISSN: 1593-8883
Electronic ISSN: 1129-6569
DOI
https://doi.org/10.1007/s10203-019-00235-0

Other articles of this Issue 1/2020

Decisions in Economics and Finance 1/2020 Go to the issue