scholarly journals Numerical method for optimal stopping of piecewise deterministic Markov processes

2010 ◽  
Vol 20 (5) ◽  
pp. 1607-1637 ◽  
Author(s):  
Benoîte de Saporta ◽  
François Dufour ◽  
Karen Gonzalez
Keyword(s):  
Numerical Method ◽  
Markov Processes ◽  
Optimal Stopping ◽  
Piecewise Deterministic Markov Processes

scholarly journals Optimal stopping for measure-valued piecewise deterministic Markov processes

2020 ◽  
Vol 57 (2) ◽  
pp. 497-512
Author(s):  
Bertrand Cloez ◽  
Benoîte de Saporta ◽  
Maud Joubaud
Keyword(s):  
Markov Processes ◽  
Optimal Stopping ◽  
Small Population ◽  
Individual Characteristics ◽  
Locally Finite ◽  
Counter Example ◽  
Random Horizon ◽  
Piecewise Deterministic Markov Processes ◽  
Point Measure ◽  
Finite Measures

AbstractThis paper investigates the random horizon optimal stopping problem for measure-valued piecewise deterministic Markov processes (PDMPs). This is motivated by population dynamics applications, when one wants to monitor some characteristics of the individuals in a small population. The population and its individual characteristics can be represented by a point measure. We first define a PDMP on a space of locally finite measures. Then we define a sequence of random horizon optimal stopping problems for such processes. We prove that the value function of the problems can be obtained by iterating some dynamic programming operator. Finally we prove via a simple counter-example that controlling the whole population is not equivalent to controlling a random lineage.

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