scholarly journals Singular Stochastic Control and Optimal Stopping with Partial Information of Itô--Lévy Processes

2012 ◽  
Vol 50 (4) ◽  
pp. 2254-2287 ◽  
Author(s):  
Bernt Øksendal ◽  
Agnès Sulem
Keyword(s):  
Stochastic Control ◽  
Optimal Stopping ◽  
Lévy Processes ◽  
Partial Information ◽  
Levy Processes ◽  
Singular Stochastic Control

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.

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
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