Duality for Multiple Stopping

2018 ◽  
pp. 177-187
Author(s):  
Denis Belomestny ◽  
John Schoenmakers
Keyword(s):  
Multiple Stopping

scholarly journals Selecting a sequence of last successes in independent trials

2000 ◽  
Vol 37 (2) ◽  
pp. 389-399 ◽  
Author(s):  
F. Thomas Bruss ◽  
Davy Paindaveine
Keyword(s):  
Approximate Solution ◽  
Convenient Method ◽  
Probability Space ◽  
Maximum Probability ◽  
Optimal Rule ◽  
Unknown Number ◽  
Multiple Stopping ◽  
Indicator Functions ◽  
Independent Indicator ◽  
Independent Trials

Let I1,I2,…,In be a sequence of independent indicator functions defined on a probability space (Ω, A, P). We say that index k is a success time if Ik = 1. The sequence I1,I2,…,In is observed sequentially. The objective of this article is to predict the lth last success, if any, with maximum probability at the time of its occurrence. We find the optimal rule and discuss briefly an algorithm to compute it in an efficient way. This generalizes the result of Bruss (1998) for l = 1, and is equivalent to the problem of (multiple) stopping with l stops on the last l successes. We then extend the model to a larger class allowing for an unknown number N of indicator functions, and present, in particular, a convenient method for an approximate solution if the success probabilities are small. We also discuss some applications of the results.

A Multiple Stopping Problem

1994 ◽  
Vol 8 (2) ◽  
pp. 169-177 ◽  
Author(s):  
J. Preater
Keyword(s):  
Optimal Stopping ◽  
Stopping Rule ◽  
Reward Function ◽  
Optimal Stopping Rule ◽  
Multiple Stopping ◽  
Constant Observation ◽  
Independent And Identically Distributed

In the context of team recruitment, we discuss an optimal multiple stopping problem for an infinite independent and identically distributed sequence, with general reward function and constant observation cost. We establish the existence and nature of an optimal stopping rule. For the particular case where team quality is governed by the fitness of the weakest member, we show that the recruiter should be more discriminating with either a better, or a larger, group of appointees in hand.

scholarly journals Optimal Buy/Sell Rules for Correlated Random Walks

2008 ◽  
Vol 45 (01) ◽  
pp. 33-44 ◽  
Author(s):  
Pieter Allaart ◽  
Michael Monticino
Keyword(s):  
Random Walks ◽  
Negative Reinforcement ◽  
Optimal Strategies ◽  
Trading Strategies ◽  
Stock Index ◽  
Elementary Model ◽  
Correlated Random Walks ◽  
Multiple Stopping ◽  
Stop Rules ◽  
Random Step

Correlated random walks provide an elementary model for processes that exhibit directional reinforcement behavior. This paper develops optimal multiple stopping strategies - buy/sell rules - for correlated random walks. The work extends previous results given in Allaart and Monticino (2001) by considering random step sizes and allowing possibly negative reinforcement of the walk's current direction. The optimal strategies fall into two general classes - cases where conservative buy-and-hold type strategies are optimal and cases for which it is optimal to follow aggressive trading strategies of successively buying and selling the commodity depending on whether the price goes up or down. Simulation examples are given based on a stock index fund to illustrate the variation in return possible using the theoretically optimal stop rules compared to simpler buy-and-hold strategies.

On multiple stopping bales

Optimization ◽  
1985 ◽  
Vol 16 (3) ◽  
pp. 401-418 ◽  
Author(s):  
W. Stadje
Keyword(s):  
Multiple Stopping

scholarly journals Numerical methods for an optimal multiple stopping problem

2016 ◽  
Vol 16 (05) ◽  
pp. 1650016 ◽  
Author(s):  
Imène Ben Latifa ◽  
Joseph Fréderic Bonnans ◽  
Mohamed Mnif
Keyword(s):  
Numerical Scheme ◽  
Value Function ◽  
Numerical Solutions ◽  
Conditional Expectations ◽  
Dynamic Programing ◽  
Optimal Quantization ◽  
Swing Option ◽  
Multiple Stopping ◽  
Viscosity Sense ◽  
The Value Function

This paper deals with numerical solutions to an optimal multiple stopping problem. The corresponding dynamic programing (DP) equation is a variational inequality satisfied by the value function in the viscosity sense. The convergence of the numerical scheme is shown by viscosity arguments. An optimal quantization method is used for computing the conditional expectations arising in the DP equation. Numerical results are presented for the price of swing option and the behavior of the value function.

scholarly journals Optimal Insurance Purchase Strategies via Optimal Multiple Stopping Times

2014 ◽  
Author(s):  
Rodrigo S Targino ◽  
Gareth William Peters ◽  
Georgy Sofronov ◽  
Pavel V. Shevchenko
Keyword(s):  
Stopping Times ◽  
Optimal Insurance ◽  
Multiple Stopping
Sign in / Sign up

Export Citation Format

Share Document