scholarly journals On approximative solutions of optimal stopping problems

2011 ◽  
Vol 43 (04) ◽  
pp. 1086-1108
Author(s):  
Andreas Faller ◽  
Ludger Rüschendorf
Keyword(s):  
Discrete Time ◽  
Extreme Value Theory ◽  
Optimal Stopping ◽  
Value Theory ◽  
Threshold Functions ◽  
Convergence Results ◽  
Process Convergence ◽  
Complete Discussion ◽  
Optimal Stopping Problems ◽  
Poisson Type

In this paper we establish an extension of the method of approximating optimal discrete-time stopping problems by related limiting stopping problems for Poisson-type processes. This extension allows us to apply this method to a larger class of examples, such as those arising, for example, from point process convergence results in extreme value theory. Furthermore, we develop new classes of solutions of the differential equations which characterize optimal threshold functions. As a particular application, we give a fairly complete discussion of the approximative optimal stopping behavior of independent and identically distributed sequences with discount and observation costs.

scholarly journals On approximative solutions of optimal stopping problems

2011 ◽  
Vol 43 (4) ◽  
pp. 1086-1108 ◽  
Author(s):  
Andreas Faller ◽  
Ludger Rüschendorf
Keyword(s):  
Discrete Time ◽  
Extreme Value Theory ◽  
Optimal Stopping ◽  
Value Theory ◽  
Threshold Functions ◽  
Convergence Results ◽  
Process Convergence ◽  
Complete Discussion ◽  
Optimal Stopping Problems ◽  
Poisson Type

In this paper we establish an extension of the method of approximating optimal discrete-time stopping problems by related limiting stopping problems for Poisson-type processes. This extension allows us to apply this method to a larger class of examples, such as those arising, for example, from point process convergence results in extreme value theory. Furthermore, we develop new classes of solutions of the differential equations which characterize optimal threshold functions. As a particular application, we give a fairly complete discussion of the approximative optimal stopping behavior of independent and identically distributed sequences with discount and observation costs.

Limit theorems for suprema, threshold-stopped random variables and last exits of i.i.d. random variables with costs and discounting, with applications to optimal stopping

1992 ◽  
Vol 24 (02) ◽  
pp. 241-266
Author(s):  
Douglas P. Kennedy ◽  
Robert P. Kertz
Keyword(s):  
Optimal Stopping ◽  
Limit Theorems ◽  
Continuous Mapping ◽  
Random Variables ◽  
Exit Times ◽  
Convergence Results ◽  
Process Convergence ◽  
Optimal Stopping Problems ◽  
The Cost ◽  
Linear Cost

For linear-cost-adjusted and geometric-discounted infinite sequences of i.i.d. random variables, point process convergence results are proved as the cost or discounting effect diminishes. These process convergence results are combined with continuous-mapping principles to obtain results on joint convergence of suprema and threshold-stopped random variables, and last-exit times and locations. Applications are made to several classical optimal stopping problems in these settings.

Limit theorems for suprema, threshold-stopped random variables and last exits of i.i.d. random variables with costs and discounting, with applications to optimal stopping

1992 ◽  
Vol 24 (2) ◽  
pp. 241-266 ◽  
Author(s):  
Douglas P. Kennedy ◽  
Robert P. Kertz
Keyword(s):  
Optimal Stopping ◽  
Limit Theorems ◽  
Continuous Mapping ◽  
Random Variables ◽  
Exit Times ◽  
Convergence Results ◽  
Process Convergence ◽  
Optimal Stopping Problems ◽  
The Cost ◽  
Linear Cost

For linear-cost-adjusted and geometric-discounted infinite sequences of i.i.d. random variables, point process convergence results are proved as the cost or discounting effect diminishes. These process convergence results are combined with continuous-mapping principles to obtain results on joint convergence of suprema and threshold-stopped random variables, and last-exit times and locations. Applications are made to several classical optimal stopping problems in these settings.

scholarly journals On general optimal stopping problems using penalty method

2012 ◽  
Vol 45 (2) ◽  
Author(s):  
Ł. Stettner
Keyword(s):  
Stochastic Processes ◽  
Markov Processes ◽  
Discrete Time ◽  
Optimal Stopping ◽  
Penalty Method ◽  
Value Function ◽  
Polish Space ◽  
Finite Horizon ◽  
Optimal Stopping Problem ◽  
Optimal Stopping Problems

AbstractIn the paper we use penalty method to approximate a number of general stopping problems over finite horizon. We consider optimal stopping of discrete time or right continuous stochastic processes, and show that suitable version of Snell’s envelope can by approximated by solutions to penalty equations. Then we study optimal stopping problem for Markov processes on a general Polish space, and again show that the optimal stopping value function can be approximated by a solution to a Markov version of the penalty equation.

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