On Wald Optimal Stopping Problem for Geometric Brownian Motions

2008 ◽  
Vol 27 (4) ◽  
pp. 435-440 ◽  
Author(s):  
Cloud Makasu
Keyword(s):  
Optimal Stopping ◽  
Optimal Stopping Problem ◽  
Brownian Motions ◽  
Geometric Brownian Motions

scholarly journals The generalized perpetual American exchange-option problem

2008 ◽  
Vol 40 (1) ◽  
pp. 163-182 ◽  
Author(s):  
Shek-Keung Tony Wong
Keyword(s):  
Optimal Stopping ◽  
First Passage Time ◽  
Passage Time ◽  
Optimal Stopping Problem ◽  
Full Generality ◽  
Investment Timing ◽  
Current Context ◽  
Geometric Brownian Motions ◽  
Underlying Processes

This paper revisits a general optimal stopping problem that often appears as a special case in some finance applications. The problem is essentially of the same form as the investment-timing problem of McDonald and Siegel (1986) in which the underlying processes are two correlated geometric Brownian motions (GBMs) with drifts less than the discount rate. By contrast, we attempt to analyze the underlying optimal stopping problem to its full generality without imposing any restriction on the drifts of the GBMs. By extending the first passage time approach of Xia and Zhou (2007) to the current context, we manage to obtain a complete and explicit characterization of the solution to the problem on all possible drift domains. Our analysis leads to a new and interesting observation that the underlying optimal stopping problem admits a two-sided optimal continuation region on some certain parameter domains.

The generalized perpetual American exchange-option problem

2008 ◽  
Vol 40 (01) ◽  
pp. 163-182 ◽  
Author(s):  
Shek-Keung Tony Wong
Keyword(s):  
Optimal Stopping ◽  
First Passage Time ◽  
Passage Time ◽  
Optimal Stopping Problem ◽  
Full Generality ◽  
Investment Timing ◽  
Current Context ◽  
Geometric Brownian Motions ◽  
Underlying Processes

This paper revisits a general optimal stopping problem that often appears as a special case in some finance applications. The problem is essentially of the same form as the investment-timing problem of McDonald and Siegel (1986) in which the underlying processes are two correlated geometric Brownian motions (GBMs) with drifts less than the discount rate. By contrast, we attempt to analyze the underlying optimal stopping problem to its full generality without imposing any restriction on the drifts of the GBMs. By extending the first passage time approach of Xia and Zhou (2007) to the current context, we manage to obtain a complete and explicit characterization of the solution to the problem on all possible drift domains. Our analysis leads to a new and interesting observation that the underlying optimal stopping problem admits a two-sided optimal continuation region on some certain parameter domains.

scholarly journals On a simple optimal stopping problem

1973 ◽  
Vol 5 (4) ◽  
pp. 297-312 ◽  
Author(s):  
William M. Boyce
Keyword(s):  
Optimal Stopping ◽  
Optimal Stopping Problem

A Note on a Lower Bound for the Multiplicative Odds Theorem of Optimal Stopping

2014 ◽  
Vol 51 (03) ◽  
pp. 885-889 ◽  
Author(s):  
Tomomi Matsui ◽  
Katsunori Ano
Keyword(s):  
Lower Bound ◽  
Optimal Stopping ◽  
Secretary Problem ◽  
Bernoulli Trials ◽  
Optimal Stopping Problem ◽  
Maximum Probability ◽  
Optimal Stopping Rule ◽  
Optimal Probability ◽  
Optimal Stopping Theory ◽  
Special Case

In this note we present a bound of the optimal maximum probability for the multiplicative odds theorem of optimal stopping theory. We deal with an optimal stopping problem that maximizes the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length N, where m and N are predetermined integers satisfying 1 ≤ m < N. This problem is an extension of Bruss' (2000) odds problem. In a previous work, Tamaki (2010) derived an optimal stopping rule. We present a lower bound of the optimal probability. Interestingly, our lower bound is attained using a variation of the well-known secretary problem, which is a special case of the odds problem.

The Optimal Stopping Problem

1969 ◽  
pp. 87-145
Author(s):  
Evgenii B. Dynkin ◽  
Aleksandr A. Yushkevich
Keyword(s):  
Optimal Stopping ◽  
Optimal Stopping Problem
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