Optimal Stopping for Lévy Processes with One-Sided Solutions

2016 ◽  
Vol 54 (5) ◽  
pp. 2553-2567 ◽  
Author(s):  
Ernesto Mordecki ◽  
Yuliya Mishura
Keyword(s):  
Optimal Stopping ◽  
Lévy Processes ◽  
Levy Processes

scholarly journals Optimal stopping of Hunt and Lévy processes

Stochastics ◽  
2007 ◽  
Vol 79 (3-4) ◽  
pp. 233-251 ◽  
Author(s):  
Ernesto Mordecki ◽  
Paavo Salminen
Keyword(s):  
Optimal Stopping ◽  
Lévy Processes ◽  
Levy Processes

Variance Optimal Stopping for Geometric Lévy Processes

2015 ◽  
Vol 47 (01) ◽  
pp. 128-145 ◽  
Author(s):  
Kamille Sofie Tågholt Gad ◽  
Jesper Lund Pedersen
Keyword(s):  
Optimal Stopping ◽  
Lévy Process ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Stopping Times ◽  
Optimal Stopping Problem ◽  
Maximum Variance ◽  
Geometric Levy Process

The main result of this paper is the solution to the optimal stopping problem of maximizing the variance of a geometric Lévy process. We call this problem the variance problem. We show that, for some geometric Lévy processes, we achieve higher variances by allowing randomized stopping. Furthermore, for some geometric Lévy processes, the problem has a solution only if randomized stopping is allowed. When randomized stopping is allowed, we give a solution to the variance problem. We identify the Lévy processes for which the allowance of randomized stopping times increases the maximum variance. When it does, we also solve the variance problem without randomized stopping.

Variance Optimal Stopping for Geometric Lévy Processes

2015 ◽  
Vol 47 (1) ◽  
pp. 128-145 ◽  
Author(s):  
Kamille Sofie Tågholt Gad ◽  
Jesper Lund Pedersen
Keyword(s):  
Optimal Stopping ◽  
Lévy Process ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Stopping Times ◽  
Optimal Stopping Problem ◽  
Maximum Variance ◽  
Geometric Levy Process

The main result of this paper is the solution to the optimal stopping problem of maximizing the variance of a geometric Lévy process. We call this problem the variance problem. We show that, for some geometric Lévy processes, we achieve higher variances by allowing randomized stopping. Furthermore, for some geometric Lévy processes, the problem has a solution only if randomized stopping is allowed. When randomized stopping is allowed, we give a solution to the variance problem. We identify the Lévy processes for which the allowance of randomized stopping times increases the maximum variance. When it does, we also solve the variance problem without randomized stopping.

scholarly journals One-sided solutions for optimal stopping problems with logconcave reward functions

2019 ◽  
Vol 51 (01) ◽  
pp. 87-115
Author(s):  
Yi-Shen Lin ◽  
Yi-Ching Yao
Keyword(s):  
Random Walks ◽  
Optimal Stopping ◽  
Lévy Processes ◽  
Levy Processes ◽  
Stopping Times ◽  
Reward Function ◽  
Continuous Reward ◽  
Optimal Stopping Problems ◽  
Reward Functions ◽  
Optimal Stopping Times

AbstractIn the literature on optimal stopping, the problem of maximizing the expected discounted reward over all stopping times has been explicitly solved for some special reward functions (including (x+)ν, (ex − K)+, (K − e− x)+, x ∈ ℝ, ν ∈ (0, ∞), and K > 0) under general random walks in discrete time and Lévy processes in continuous time (subject to mild integrability conditions). All such reward functions are continuous, increasing, and logconcave while the corresponding optimal stopping times are of threshold type (i.e. the solutions are one-sided). In this paper we show that all optimal stopping problems with increasing, logconcave, and right-continuous reward functions admit one-sided solutions for general random walks and Lévy processes, thereby generalizing the aforementioned results. We also investigate in detail the principle of smooth fit for Lévy processes when the reward function is increasing and logconcave.

Sign in / Sign up

Export Citation Format

Share Document