Explicit solution of an optimal stopping problem: the burn-in of conditionally exponential components

1997 ◽  
Vol 34 (1) ◽  
pp. 267-282 ◽  
Author(s):  
C. Costantini ◽  
F. Spizzichino
Keyword(s):  
Markov Process ◽  
Statistical Model ◽  
Optimal Stopping ◽  
Continuous Time ◽  
Explicit Solution ◽  
Prior Distribution ◽  
Unknown Parameter ◽  
Two Dimensional ◽  
Optimal Stopping Problem ◽  
Optimal Duration

We consider the problem of the optimal duration of a burn-in experiment for n identical units with conditionally exponential life-times of unknown parameter Λ. The problem is formulated as an optimal stopping problem for a suitably defined two-dimensional continuous-time Markov process. By exploiting monotonicity properties of the statistical model and of the costs we prove that the optimal stopping region is monotone (according to an appropriate definition) and derive a set of equations that uniquely determine it and that can be easily solved recursively. The optimal stopping region varies monotonically with the costs. For the class of problems corresponding to a prior distribution on Λ of type gamma it is shown how the optimal stopping region varies with respect to the prior distribution and with respect to n.

Explicit solution of an optimal stopping problem: the burn-in of conditionally exponential components

1997 ◽  
Vol 34 (01) ◽  
pp. 267-282
Author(s):  
C. Costantini ◽  
F. Spizzichino
Keyword(s):  
Markov Process ◽  
Statistical Model ◽  
Optimal Stopping ◽  
Continuous Time ◽  
Explicit Solution ◽  
Prior Distribution ◽  
Unknown Parameter ◽  
Two Dimensional ◽  
Optimal Stopping Problem ◽  
Optimal Duration

We consider the problem of the optimal duration of a burn-in experiment for n identical units with conditionally exponential life-times of unknown parameter Λ. The problem is formulated as an optimal stopping problem for a suitably defined two-dimensional continuous-time Markov process. By exploiting monotonicity properties of the statistical model and of the costs we prove that the optimal stopping region is monotone (according to an appropriate definition) and derive a set of equations that uniquely determine it and that can be easily solved recursively. The optimal stopping region varies monotonically with the costs. For the class of problems corresponding to a prior distribution on Λ of type gamma it is shown how the optimal stopping region varies with respect to the prior distribution and with respect to n.

scholarly journals An Optimal Stopping Problem for Jump Diffusion Logistic Population Model

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Yang Sun ◽  
Xiaohui Ai
Keyword(s):  
Optimal Stopping ◽  
Critical State ◽  
Explicit Solution ◽  
Population Model ◽  
Value Function ◽  
Jump Diffusion ◽  
Optimal Value Function ◽  
Optimal Stopping Problem ◽  
Optimal Value ◽  
Poisson Jump

This paper examines an optimal stopping problem for the stochastic (Wiener-Poisson) jump diffusion logistic population model. We present an explicit solution to an optimal stopping problem of the stochastic (Wiener-Poisson) jump diffusion logistic population model by applying the smooth pasting technique (Dayanik and Karatzas, 2003; Dixit, 1993). We formulate this as an optimal stopping problem of maximizing the expected reward. We express the critical state of the optimal stopping region and the optimal value function explicitly.

An Optimal Stopping Problem Arising from a Decision Model with Many Agents

1998 ◽  
Vol 12 (3) ◽  
pp. 393-408 ◽  
Author(s):  
Bruno Bassan ◽  
Claudia Ceci
Keyword(s):  
Markov Process ◽  
Stefan Problem ◽  
Optimal Stopping ◽  
Economic Model ◽  
Decision Model ◽  
Value Function ◽  
Lower Semicontinuous ◽  
Social Planner ◽  
Optimal Stopping Problem ◽  
Reward Function

We study an optimal stopping problem for a nonhomogeneous Markov process, with a reward function that is lower semicontinuous everywhere and smooth in certain regions. We prove that the payoff (value function) is lower semicontinuous as well and solves a so-called generalized Stefan problem in each of these regions. We provide some results for the geometry of the “stopping observations” set. Our results generalize those in Bassan, Brezzi, and Scarsini (1996). The problem we consider stems from an economic model in which several self-interested agents desire information, whereas a social planner, although benevolent toward the agents, might decide to withhold information in order to induce diversification in their behavior.

scholarly journals Value Function and Optimal Rule on the Optimal Stopping Problem for Continuous-Time Markov Processes

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Lu Ye
Keyword(s):  
Explicit Formula ◽  
Markov Processes ◽  
Optimal Stopping ◽  
Continuous Time ◽  
Value Function ◽  
Broad Class ◽  
Stopping Time ◽  
Optimal Stopping Problem ◽  
Optimal Rule ◽  
Reward Functions

This paper considers the optimal stopping problem for continuous-time Markov processes. We describe the methodology and solve the optimal stopping problem for a broad class of reward functions. Moreover, we illustrate the outcomes by some typical Markov processes including diffusion and Lévy processes with jumps. For each of the processes, the explicit formula for value function and optimal stopping time is derived. Furthermore, we relate the derived optimal rules to some other optimal problems.

Optimal Stopping in a Dice Game

1998 ◽  
Vol 35 (01) ◽  
pp. 229-235 ◽  
Author(s):  
Markus Roters
Keyword(s):  
Optimal Stopping ◽  
Explicit Solution ◽  
Stopping Rule ◽  
Optimal Stopping Problem ◽  
Optimal Stopping Rule ◽  
Rules Of The Game

In this paper we consider an explicit solution of an optimal stopping problem arising in connection with a dice game. An optimal stopping rule and the maximum expected reward in this problem can easily be computed by means of the distributions involved and the specific rules of the game

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