Optimal stopping for general random walks

2007 ◽  
pp. 133-166
Keyword(s):  
Random Walks ◽  
Optimal Stopping

Optimal Stopping Time for Geometric Random Walks with Power Payoff Function

2020 ◽  
Vol 81 (7) ◽  
pp. 1192-1210
Author(s):  
O.V. Zverev ◽  
V.M. Khametov ◽  
E.A. Shelemekh
Keyword(s):  
Random Walks ◽  
Optimal Stopping ◽  
Stopping Time ◽  
Payoff Function ◽  
Optimal Stopping Time

Optimal stopping rules for correlated random walks with a discount

2004 ◽  
Vol 41 (2) ◽  
pp. 483-496 ◽  
Author(s):  
Pieter Allaart
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Optimal Stopping ◽  
Constant Factor ◽  
Stopping Rules ◽  
Correlated Random Walk ◽  
Numerical Examples ◽  
Optimal Rule ◽  
Correlated Random Walks ◽  
Optimal Stopping Rules

Optimal stopping rules are developed for the correlated random walk when future returns are discounted by a constant factor per unit time. The optimal rule is shown to be of dual threshold form: one threshold for stopping after an up-step, and another for stopping after a down-step. Precise expressions for the thresholds are given for both the positively and the negatively correlated cases. The optimal rule is illustrated by several numerical examples.

Optimal Stopping of Observations in Control Problems for Random Walks

1991 ◽  
Vol 35 (4) ◽  
pp. 746-753
Author(s):  
S. V. Vinnichenko ◽  
V. V. Mazalov
Keyword(s):  
Random Walks ◽  
Optimal Stopping ◽  
Control Problems

FINITE HORIZON RUIN PROBABILITIES FOR RANDOM WALKS WITH HEAVY TAILED INCREMENTS

2013 ◽  
Vol 27 (2) ◽  
pp. 237-246
Author(s):  
Yingdong Lu
Keyword(s):  
Asymptotic Behavior ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
Optimal Stopping ◽  
Fourier Transformation ◽  
Main Idea ◽  
Finite Horizon ◽  
Ruin Probabilities ◽  
Heavy Tailed

We study the asymptotic behavior of finite horizon ruin probabilities for random walks with heavy tailed increment via corrected diffusion approximation. We follow the main idea in [4] of inverting Fourier transformation, and the Fourier transformation is calculated through optimal stopping and a central limit theorem for renewal process.

A Game with Optimal Stopping of Random Walks

1998 ◽  
Vol 42 (4) ◽  
pp. 697-701
Author(s):  
V. V. Mazalov E. A. Kochetov
Keyword(s):  
Random Walks ◽  
Optimal 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.

scholarly journals Random Walks and Optimal Stopping Strategies as a Model for Evolving Networks

2013 ◽  
Vol 410 ◽  
pp. 012092 ◽  
Author(s):  
D S Vlachos ◽  
K J Parousis-Orthodoxou ◽  
M M Stamos
Keyword(s):  
Random Walks ◽  
Optimal Stopping ◽  
Evolving Networks
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