scholarly journals A finite exact algorithm to solve a dice game

2016 ◽  
Vol 53 (1) ◽  
pp. 91-105
Author(s):  
Fabián Crocce ◽  
Ernesto Mordecki
Keyword(s):  
Optimal Stopping ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Exact Algorithm ◽  
Critical Threshold ◽  
Control Processes ◽  
Optimal Stopping Problems ◽  
Continuous Time Processes ◽  
Markov Control Processes ◽  
Markov Control

Abstract We provide an algorithm to find the value and an optimal strategy of the Ten Thousand dice game solitaire variant in the framework of Markov control processes. Once an optimal critical threshold is found, the set of nonstopping states of the game becomes finite and the solution is found by a backwards algorithm that gives the values for each one of these states of the game. The algorithm is finite and exact. The strategy to find the critical threshold comes from the continuous pasting condition used in optimal stopping problems for continuous-time processes with jumps.

Constrained Continuous-Time Markov Control Processes with Discounted Criteria

2003 ◽  
Vol 21 (2) ◽  
pp. 379-399 ◽  
Author(s):  
Xianping Guo ◽  
Onésimo Hernández-Lerma
Keyword(s):  
Continuous Time ◽  
Control Processes ◽  
Markov Control Processes ◽  
Markov Control

scholarly journals Robust Markov control processes

2014 ◽  
Vol 420 (2) ◽  
pp. 1337-1353 ◽  
Author(s):  
Anna Jaśkiewicz ◽  
Andrzej S. Nowak
Keyword(s):  
Control Processes ◽  
Markov Control Processes ◽  
Markov Control

Markov control processes with pathwise constraints

2010 ◽  
Vol 71 (3) ◽  
pp. 477-502 ◽  
Author(s):  
Armando F. Mendoza-Pérez ◽  
Onésimo Hernández-Lerma
Keyword(s):  
Control Processes ◽  
Markov Control Processes ◽  
Markov Control

Semi-Markov Control Processes with Unknown Holding Times Distribution Under an Average Cost Criterion

2009 ◽  
Vol 61 (3) ◽  
pp. 317-336 ◽  
Author(s):  
Fernando Luque-Vásquez ◽  
J. Adolfo Minjárez-Sosa ◽  
Luz del Carmen Rosas-Rosas
Keyword(s):  
Average Cost ◽  
Average Cost Criterion ◽  
Control Processes ◽  
Cost Criterion ◽  
Markov Control Processes ◽  
Markov Control

Optimal strategies for discovering new species in continuous time

1989 ◽  
Vol 26 (04) ◽  
pp. 695-706
Author(s):  
Gerold Alsmeyer ◽  
Albrecht Irle
Keyword(s):  
New Species ◽  
Optimal Stopping ◽  
Continuous Time ◽  
Optimal Strategy ◽  
Stopping Time ◽  
Optimal Strategies ◽  
Distinct Species ◽  
Natural Generalization ◽  
General Point ◽  
Time Optimal

Consider a population of distinct species Sj , j∈J, members of which are selected at different time points T 1 , T 2,· ··, one at each time. Assume linear costs per unit of time and that a reward is earned at each discovery epoch of a new species. We treat the problem of finding a selection rule which maximizes the expected payoff. As the times between successive selections are supposed to be continuous random variables, we are dealing with a continuous-time optimal stopping problem which is the natural generalization of the one Rasmussen and Starr (1979) have investigated; namely, the corresponding problem with fixed times between successive selections. However, in contrast to their discrete-time setting the derivation of an optimal strategy appears to be much harder in our model as generally we are no longer in the monotone case. This note gives a general point process formulation for this problem, leading in particular to an equivalent stopping problem via stochastic intensities which is easier to handle. Then we present a formal derivation of the optimal stopping time under the stronger assumption of i.i.d. (X 1 , A 1) (X2, A2 ), · ·· where Xn gives the label (j for Sj ) of the species selected at Tn and An denotes the time between the nth and (n – 1)th selection, i.e. An = Tn – Tn– 1. In the case where even Xn and An are independent and An has an IFR (increasing failure rate) distribution, an explicit solution for the optimal strategy is derived as a simple consequence.

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