Solution of the Optimal Stopping Problem for One-Dimensional Diffusion Based on a Modification of the Payoff Function

2012 ◽  
pp. 371-403 ◽  
Author(s):  
Ernst Presman
Keyword(s):  
Optimal Stopping ◽  
Payoff Function ◽  
Optimal Stopping Problem ◽  
One Dimensional ◽  
Dimensional Diffusion

On the threshold strategies in optimal stopping problems for diffusion processes

2017 ◽  
Vol 54 (3) ◽  
pp. 963-969 ◽  
Author(s):  
Vadim Arkin ◽  
Alexander Slastnikov
Keyword(s):  
Diffusion Process ◽  
Optimal Stopping ◽  
Diffusion Processes ◽  
Sufficient Conditions ◽  
Payoff Function ◽  
Threshold Strategy ◽  
One Dimensional ◽  
Stopping Set ◽  
Optimal Stopping Problems ◽  
Necessary And Sufficient

Abstract We study a problem when the optimal stopping for a one-dimensional diffusion process is generated by a threshold strategy. Namely, we give necessary and sufficient conditions (on the diffusion process and the payoff function) under which a stopping set has a threshold structure.

Optimal Closing of a Momentum Trade

2013 ◽  
Vol 50 (02) ◽  
pp. 374-387 ◽  
Author(s):  
Erik Ekström ◽  
Carl Lindberg
Keyword(s):  
Optimal Stopping ◽  
Asset Price ◽  
Optimal Timing ◽  
Model Parameters ◽  
Optimal Stopping Problem ◽  
One Dimensional ◽  
Academic Literature ◽  
Holding Period ◽  
The Past ◽  
Asset Sale

There is an extensive academic literature that documents that stocks which have performed well in the past often continue to perform well over some holding period - so-called momentum. We study the optimal timing for an asset sale for an agent with a long position in a momentum trade. The asset price is modelled as a geometric Brownian motion with a drift that initially exceeds the discount rate, but with the opposite relation after an unobservable and exponentially distributed time. The problem of optimal selling of the asset is then formulated as an optimal stopping problem under incomplete information. Based on the observations of the asset, the agent wants to detect the unobservable change point as accurately as possible. Using filtering techniques and stochastic analysis, we reduce the problem to a one-dimensional optimal stopping problem, which we solve explicitly. We also show that the optimal boundary at which the investor should liquidate the trade depends monotonically on the model parameters.

scholarly journals On an Approximation Order of the Optimal Stopping Problem for 𝑛-Dimensional Diffusion Processes

2005 ◽  
Vol 12 (4) ◽  
pp. 693-696
Author(s):  
Giorgi Lominashvili
Keyword(s):  
Optimal Stopping ◽  
Diffusion Processes ◽  
Approximation Order ◽  
Optimal Stopping Problem ◽  
Dimensional Diffusion ◽  
Multidimensional Diffusion

Abstract An approximation order of the optimal stopping problem for multidimensional diffusion processes by the corresponding semidiscretization is considered.

On a stopping problem involving refusal and forced stopping

1983 ◽  
Vol 20 (1) ◽  
pp. 71-81 ◽  
Author(s):  
Masami Yasuda
Keyword(s):  
Conditional Probability ◽  
Markov Decision Process ◽  
Optimal Stopping ◽  
Decision Process ◽  
Slight Modification ◽  
Optimal Stopping Problem ◽  
Choice Problem ◽  
One Dimensional ◽  
Markov Decision ◽  
The One

Although the usual optimal stopping problem is described as a Markov decision process with two decisions, stop and continue, we shall consider a model which distinguishes the observer's strategy from the system's two decisions. The observer can select a strategy defined on an action space, and the decision of the system to stop or continue is determined by a prescribed conditional probability. For this model, it may happen that the strategy (a) to stop is refused, or (b) to continue is forcibly stopped. This is a slight modification of the one-dimensional stopping problem by involving refusal and forced stopping. The model is motivated by the uncertain secretary choice problem of Smith (1975) and the multivariate stopping problem of Kurano, Yasuda and Nakagami (1980), (1982).

On a stopping problem involving refusal and forced stopping

1983 ◽  
Vol 20 (01) ◽  
pp. 71-81
Author(s):  
Masami Yasuda
Keyword(s):  
Conditional Probability ◽  
Markov Decision Process ◽  
Optimal Stopping ◽  
Decision Process ◽  
Slight Modification ◽  
Optimal Stopping Problem ◽  
Choice Problem ◽  
One Dimensional ◽  
Markov Decision ◽  
The One

Although the usual optimal stopping problem is described as a Markov decision process with two decisions, stop and continue, we shall consider a model which distinguishes the observer's strategy from the system's two decisions. The observer can select a strategy defined on an action space, and the decision of the system to stop or continue is determined by a prescribed conditional probability. For this model, it may happen that the strategy (a) to stop is refused, or (b) to continue is forcibly stopped. This is a slight modification of the one-dimensional stopping problem by involving refusal and forced stopping. The model is motivated by the uncertain secretary choice problem of Smith (1975) and the multivariate stopping problem of Kurano, Yasuda and Nakagami (1980), (1982).

scholarly journals Optimal Closing of a Momentum Trade

2013 ◽  
Vol 50 (2) ◽  
pp. 374-387 ◽  
Author(s):  
Erik Ekström ◽  
Carl Lindberg
Keyword(s):  
Optimal Stopping ◽  
Asset Price ◽  
Optimal Timing ◽  
Model Parameters ◽  
Optimal Stopping Problem ◽  
One Dimensional ◽  
Academic Literature ◽  
Holding Period ◽  
The Past ◽  
Asset Sale

There is an extensive academic literature that documents that stocks which have performed well in the past often continue to perform well over some holding period - so-called momentum. We study the optimal timing for an asset sale for an agent with a long position in a momentum trade. The asset price is modelled as a geometric Brownian motion with a drift that initially exceeds the discount rate, but with the opposite relation after an unobservable and exponentially distributed time. The problem of optimal selling of the asset is then formulated as an optimal stopping problem under incomplete information. Based on the observations of the asset, the agent wants to detect the unobservable change point as accurately as possible. Using filtering techniques and stochastic analysis, we reduce the problem to a one-dimensional optimal stopping problem, which we solve explicitly. We also show that the optimal boundary at which the investor should liquidate the trade depends monotonically on the model parameters.

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