Cases and Studies of Security & Regulation in Lottery & Gambling
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- Article] Finite-time optimal control of a process leaving an interval
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DocNo of ILP: 7648
Doc. Type: Article
Title: Finite-time optimal control of a process leaving an interval
Authors: McBeth, DW; Weerasinghe, APN
Full Name of Authors: McBeth, DW; Weerasinghe, APN
Keywords by Author: stochastic optimal control; gambling problems; bold play; parabolic partial differential equations
Keywords Plus:
Abstract: Consider the optimal control problem of leaving an interval (-a, a) in a limited playing time. In the discrete-time problem, a is a positive integer and the player's position is given by a simple random walk on the integers with initial position x. At each time instant, the player chooses a coin from a control set where the probability of returning heads depends on the current position and the remaining amount of playing time, and the player is betting a unit value on the toss of the coin: heads returning +1 and tails -1. We discuss the optimal strategy for this discrete-time game. In the continuous-time problem the player chooses infinitesimal mean and infinitesimal variance parameters from a control set which may depend upon the player's position. The problem is to find optimal mean and variance parameters that maximize the probability of leaving the interval [-a, a] within a finite time T>0.
Cate of OECD: Mathematics
Year of Publication: 1996
Business Area: game
Detail Business: game
Country: England
Study Area: regulation, control, probability, probability, player, problem
Name of Journal: JOURNAL OF APPLIED PROBABILITY
Language: English
Country of Authors: IOWA STATE UNIV,DEPT MATH,AMES,IA 50011
Press Adress: McBeth, DW (reprint author), IOWA STATE UNIV,DEPT IND & MFG SYST ENGN,AMES,IA 50011, USA.
Email Address:
Citaion:
Funding:
Lists of Citation: Fleming W.H., 1993, CONTROLLED MARKOV PR; Friedman A., 1983, PARTIAL DIFFERENTIAL; HEATH D, 1988, ADV APPL PROBAB, V20, P635, DOI 10.2307/1427039; HEATH D, 1987, SIAM J CONTROL OPTIM, V25, P195, DOI 10.1137/0325012; HEATH D, 1974, ADV APPL PROBAB, V6, P651, DOI 10.2307/1426185; Ikeda N., 1981, STOCHASTIC DIFFERENT; KARATZAS I., 1988, BROWNIAN MOTION STOC; Ladyzhenskaya O. A., 1968, LINEAR QUASILINEAR E; LIEBERMAN GM, 1986, J MATH ANAL APPL, V113, P422, DOI 10.1016/0022-247X(86)90314-8; PESTIEN V, 1983, MATH OPER RES, V10, P599; Protter M.H., 1984, MAXIMUM PRINCIPLES D; SPENCER J, 1986, COMBINATORICA, V6, P55, DOI 10.1007/BF02579409; WEERASINGHE APN, 1992, SIAM J CONTROL OPTIM, V30, P1395, DOI 10.1137/0330074
Number of Citaion: 13
Publication: APPLIED PROBABILITY TRUST
City of Publication: SHEFFIELD
Address of Publication: THE UNIVERSITY DEPT PROB AND STATISTICS, SHEFFIELD, ENGLAND S3 7RH
ISSN: 0021-9002
29-Character Source Abbreviation: J APPL PROBAB
ISO Source Abbreviation: J. Appl. Probab.
Volume: 33
Version: 3
Start of File: 714
End of File: 728
DOI: 10.2307/3215353
Number of Pages: 15
Web of Science Category: Statistics & Probability
Subject Category: Mathematics
Document Delivery Number: VH253
Unique Article Identifier: WOS:A1996VH25300012
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