scholarly journals Stochastic mesh method for optimal stopping problems

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Yuri Kashtanov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Optimal Stopping ◽  
Jump Diffusion ◽  
Optimal Stopping Problem ◽  
Mesh Method ◽  
Consistent Estimators ◽  
Optimal Stopping Problems

AbstractA Monte Carlo method for solving the multi-dimensional optimal stopping problem is considered. Consistent estimators for a general jump-diffusion are pointed out. It is shown that the variance of estimators is inverse proportional to the number of points in each layer of the mesh.

scholarly journals A Forward Algorithm for Solving Optimal Stopping Problems

2006 ◽  
Vol 43 (01) ◽  
pp. 102-113
Author(s):  
Albrecht Irle
Keyword(s):  
State Space ◽  
Optimal Stopping ◽  
Stopping Time ◽  
The State ◽  
Optimal Stopping Problem ◽  
Forward Algorithm ◽  
Optimal Stopping Time ◽  
Entrance Time ◽  
Markov Sequence ◽  
Optimal Stopping Problems

We consider the optimal stopping problem for g(Z n ), where Z n , n = 1, 2, …, is a homogeneous Markov sequence. An algorithm, called forward improvement iteration, is presented by which an optimal stopping time can be computed. Using an iterative step, this algorithm computes a sequence B 0 ⊇ B 1 ⊇ B 2 ⊇ · · · of subsets of the state space such that the first entrance time into the intersection F of these sets is an optimal stopping time. Various applications are given.

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.

scholarly journals On Optimal Stopping Problems for Matrix-Exponential Jump-Diffusion Processes

2012 ◽  
Vol 49 (2) ◽  
pp. 531-548 ◽  
Author(s):  
Yuan-Chung Sheu ◽  
Ming-Yao Tsai
Keyword(s):  
Explicit Formula ◽  
Optimal Stopping ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Optimal Level ◽  
Matrix Exponential ◽  
Call Type ◽  
Jump Diffusion Processes ◽  
Averaging Problem ◽  
Optimal Stopping Problems

In this paper we consider optimal stopping problems for a general class of reward functions under matrix-exponential jump-diffusion processes. Given an American call-type reward function in this class, following the averaging problem approach (see, for example, Alili and Kyprianou (2005), Kyprianou and Surya (2005), Novikov and Shiryaev (2007), and Surya (2007)), we give an explicit formula for solutions of the corresponding averaging problem. Based on this explicit formula, we obtain the optimal level and the value function for American call-type optimal stopping problems.

Monotone stopping games

1987 ◽  
Vol 24 (02) ◽  
pp. 386-401 ◽  
Author(s):  
John W. Mamer
Keyword(s):  
Nash Equilibrium ◽  
Optimal Stopping ◽  
Nash Equilibria ◽  
Stopping Times ◽  
Optimal Stopping Problem ◽  
Optimal Stopping Problems ◽  
Zero Sum ◽  
Stopping Games

We consider the extension of optimal stopping problems to non-zero-sum strategic settings called stopping games. By imposing a monotone structure on the pay-offs of the game we establish the existence of a Nash equilibrium in non-randomized stopping times. As a corollary, we identify a class of games for which there are Nash equilibria in myopic stopping times. These games satisfy the strategic equivalent of the classical ‘monotone case' assumptions of the optimal stopping problem.

scholarly journals On the Continuous and Smooth Fit Principle for Optimal Stopping Problems in Spectrally Negative Lévy Models

2014 ◽  
Vol 46 (1) ◽  
pp. 139-167 ◽  
Author(s):  
Masahiko Egami ◽  
Kazutoshi Yamazaki
Keyword(s):  
Optimal Stopping ◽  
Optimal Stopping Problem ◽  
Infinite Time ◽  
Expected Payoff ◽  
Threshold Levels ◽  
Put Option ◽  
Optimal Stopping Problems ◽  
American Put ◽  
Spectrally Negative Lévy Processes ◽  
Optimal Candidate

We consider a class of infinite time horizon optimal stopping problems for spectrally negative Lévy processes. Focusing on strategies of threshold type, we write explicit expressions for the corresponding expected payoff via the scale function, and further pursue optimal candidate threshold levels. We obtain and show the equivalence of the continuous/smooth fit condition and the first-order condition for maximization over threshold levels. As examples of its applications, we give a short proof of the McKean optimal stopping problem (perpetual American put option) and solve an extension to Egami and Yamazaki (2013).

scholarly journals On Optimal Stopping Problems for Matrix-Exponential Jump-Diffusion Processes

2012 ◽  
Vol 49 (02) ◽  
pp. 531-548
Author(s):  
Yuan-Chung Sheu ◽  
Ming-Yao Tsai
Keyword(s):  
Explicit Formula ◽  
Optimal Stopping ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Optimal Level ◽  
Matrix Exponential ◽  
Call Type ◽  
Jump Diffusion Processes ◽  
Averaging Problem ◽  
Optimal Stopping Problems

In this paper we consider optimal stopping problems for a general class of reward functions under matrix-exponential jump-diffusion processes. Given an American call-type reward function in this class, following the averaging problem approach (see, for example, Alili and Kyprianou (2005), Kyprianou and Surya (2005), Novikov and Shiryaev (2007), and Surya (2007)), we give an explicit formula for solutions of the corresponding averaging problem. Based on this explicit formula, we obtain the optimal level and the value function for American call-type optimal stopping problems.

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