Degeneracy condition for the optimal moment in the optimal stopping problem for a new functional of a symmetric random walk and its maximum

2015 ◽  
Vol 70 (4) ◽  
pp. 149-159
Author(s):  
A. L. Vorob’ev
Keyword(s):  
Random Walk ◽  
Optimal Stopping ◽  
Optimal Stopping Problem ◽  
Symmetric Random Walk ◽  
Degeneracy Condition

scholarly journals Investing and Stopping

2014 ◽  
Vol 51 (4) ◽  
pp. 898-909
Author(s):  
Moritz Duembgen ◽  
L. C. G. Rogers
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Optimal Stopping ◽  
Numerical Scheme ◽  
Optimization Problem ◽  
Hedge Fund ◽  
Optimal Stopping Problem ◽  
Over Time

In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not just on the terminal value of the fund level, but also on the lowest and the highest value reached over that time. We establish equivalence to an optimal stopping problem for Brownian motion; by approximating this problem with the corresponding optimal stopping problem for a random walk we are led to a simple and efficient numerical scheme to find the solution, which we then illustrate with some examples.

Investing and Stopping

2014 ◽  
Vol 51 (04) ◽  
pp. 898-909
Author(s):  
Moritz Duembgen ◽  
L. C. G. Rogers
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Optimal Stopping ◽  
Numerical Scheme ◽  
Optimization Problem ◽  
Hedge Fund ◽  
Optimal Stopping Problem ◽  
Over Time

In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not just on the terminal value of the fund level, but also on the lowest and the highest value reached over that time. We establish equivalence to an optimal stopping problem for Brownian motion; by approximating this problem with the corresponding optimal stopping problem for a random walk we are led to a simple and efficient numerical scheme to find the solution, which we then illustrate with some examples.

Optimal stopping and embedding

2000 ◽  
Vol 37 (04) ◽  
pp. 1143-1148 ◽  
Author(s):  
Damien Lamberton ◽  
L. C. G. Rogers
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Optimal Stopping ◽  
Optimal Stopping Problem

We use embedding techniques to analyse the error of approximation of an optimal stopping problem along Brownian paths when Brownian motion is approximated by a random walk.

Optimal stopping and embedding

2000 ◽  
Vol 37 (4) ◽  
pp. 1143-1148 ◽  
Author(s):  
Damien Lamberton ◽  
L. C. G. Rogers
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Optimal Stopping ◽  
Optimal Stopping Problem

We use embedding techniques to analyse the error of approximation of an optimal stopping problem along Brownian paths when Brownian motion is approximated by a random walk.

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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