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 rules for correlated random walks with a discount

2004 ◽  
Vol 41 (02) ◽  
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 rules for directionally reinforced processes

2001 ◽  
Vol 33 (2) ◽  
pp. 483-504 ◽  
Author(s):  
Pieter Allaart ◽  
Michael Monticino
Keyword(s):  
Transaction Costs ◽  
Optimal Stopping ◽  
Optimal Strategies ◽  
Stopping Rules ◽  
Elementary Model ◽  
Numerical Examples ◽  
Special Cases ◽  
Correlated Random Walks ◽  
Multiple Stopping ◽  
Optimal Stopping Rules

This paper analyzes optimal single and multiple stopping rules for a class of correlated random walks that provides an elementary model for processes exhibiting momentum or directional reinforcement behavior. Explicit descriptions of optimal stopping rules are given in several interesting special cases with and without transaction costs. Numerical examples are presented comparing optimal strategies to simpler buy and hold strategies.

Some problems on a one-dimensional correlated random walk with various types of barrier

1992 ◽  
Vol 29 (01) ◽  
pp. 196-201 ◽  
Author(s):  
Yuan Lin Zhang
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Correlated Random Walk ◽  
Numerical Examples ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Expected Duration ◽  
Explicit Expressions

In this paper one-dimensional correlated random walks (CRW) with various types of barrier such as elastic barriers, absorbing barriers and so on are defined, and explicit expressions are derived for the ultimate absorbing probability and expected duration. Some numerical examples to illustrate the effects of correlation are also presented.

Some problems on a one-dimensional correlated random walk with various types of barrier

1992 ◽  
Vol 29 (1) ◽  
pp. 196-201 ◽  
Author(s):  
Yuan Lin Zhang
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Correlated Random Walk ◽  
Numerical Examples ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Expected Duration ◽  
Explicit Expressions

In this paper one-dimensional correlated random walks (CRW) with various types of barrier such as elastic barriers, absorbing barriers and so on are defined, and explicit expressions are derived for the ultimate absorbing probability and expected duration. Some numerical examples to illustrate the effects of correlation are also presented.

Transition probability matrices for correlated random walks

1980 ◽  
Vol 17 (01) ◽  
pp. 253-258 ◽  
Author(s):  
R. B. Nain ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Difference Equations ◽  
Generating Functions ◽  
Transition Probability ◽  
Correlated Random Walk ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Transition Probability Matrices ◽  
Probability Matrices

For correlated random walks a method of transition probability matrices as an alternative to the much-used methods of probability generating functions and difference equations has been investigated in this paper. To illustrate the use of transition probability matrices for computing the various probabilities for correlated random walks, the transition probability matrices for restricted/unrestricted one-dimensional correlated random walk have been defined and used to obtain some of the probabilities.

Return probabilities for correlated random walks

1986 ◽  
Vol 23 (1) ◽  
pp. 201-207
Author(s):  
Gillian Iossif
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Integer Lattice ◽  
Asymptotic Estimates ◽  
Correlated Random Walk ◽  
Correlated Random Walks ◽  
Previous Step

A correlated random walk on a d-dimensional integer lattice is studied in which, at any stage, the probabilities of the next step being in the various possible directions depend on the direction of the previous step. Using a renewal argument, asymptotic estimates are obtained for the probability of return to the origin after n steps.

Transition probability matrices for correlated random walks

1980 ◽  
Vol 17 (1) ◽  
pp. 253-258 ◽  
Author(s):  
R. B. Nain ◽  
Kanwar Sen
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Difference Equations ◽  
Generating Functions ◽  
Transition Probability ◽  
Correlated Random Walk ◽  
One Dimensional ◽  
Correlated Random Walks ◽  
Transition Probability Matrices ◽  
Probability Matrices

For correlated random walks a method of transition probability matrices as an alternative to the much-used methods of probability generating functions and difference equations has been investigated in this paper. To illustrate the use of transition probability matrices for computing the various probabilities for correlated random walks, the transition probability matrices for restricted/unrestricted one-dimensional correlated random walk have been defined and used to obtain some of the probabilities.

Return probabilities for correlated random walks

1986 ◽  
Vol 23 (01) ◽  
pp. 201-207 ◽  
Author(s):  
Gillian Iossif
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Integer Lattice ◽  
Asymptotic Estimates ◽  
Correlated Random Walk ◽  
Correlated Random Walks ◽  
Previous Step

A correlated random walk on a d-dimensional integer lattice is studied in which, at any stage, the probabilities of the next step being in the various possible directions depend on the direction of the previous step. Using a renewal argument, asymptotic estimates are obtained for the probability of return to the origin after n steps.

Sign in / Sign up

Export Citation Format

Share Document