scholarly journals Optimal stopping of semi-stable diffusion processes

1972 ◽  
Vol 12 (4) ◽  
pp. 99-112
Author(s):  
R. Kudžma
Keyword(s):  
Optimal Stopping ◽  
Diffusion Processes

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Р. Куджма. Оптимальная остановка полуустойчивых диффузионных процессов R. Kudžma. Pusiau stabiliųjų difuzinių procesų optimalusis stabdymas

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.

scholarly journals On Optimal Stopping Problems for Matrix-Exponential Jump-Diffusion Processes

2012 ◽  
Vol 49 (2) ◽  
pp. 531-548 ◽  
Author(s):  
Yuan-Chung Sheu ◽  
Ming-Yao Tsai
Keyword(s):  
Explicit Formula ◽  
Optimal Stopping ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Optimal Level ◽  
Matrix Exponential ◽  
Call Type ◽  
Jump Diffusion Processes ◽  
Averaging Problem ◽  
Optimal Stopping Problems

In this paper we consider optimal stopping problems for a general class of reward functions under matrix-exponential jump-diffusion processes. Given an American call-type reward function in this class, following the averaging problem approach (see, for example, Alili and Kyprianou (2005), Kyprianou and Surya (2005), Novikov and Shiryaev (2007), and Surya (2007)), we give an explicit formula for solutions of the corresponding averaging problem. Based on this explicit formula, we obtain the optimal level and the value function for American call-type optimal stopping problems.

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.

scholarly journals Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes

2007 ◽  
Vol 44 (03) ◽  
pp. 713-731 ◽  
Author(s):  
Pavel V. Gapeev
Keyword(s):  
Optimal Stopping ◽  
Diffusion Processes ◽  
Free Boundary Problems ◽  
Compound Poisson Process ◽  
Jump Diffusion ◽  
Dimensional System ◽  
Closed Form Solutions ◽  
Jump Diffusion Processes ◽  
Lookback Options ◽  
Jump Diffusion Model

In this paper we present closed form solutions of some discounted optimal stopping problems for the maximum process in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problems to integro-differential free-boundary problems, where the normal-reflection and smooth-fit conditions may break down and the latter then replaced by the continuous-fit condition. We show that, under certain relationships on the parameters of the model, the optimal stopping boundary can be uniquely determined as a component of the solution of a two-dimensional system of nonlinear ordinary differential equations. The obtained results can be interpreted as pricing perpetual American lookback options with fixed and floating strikes in a jump-diffusion model.

scholarly journals On Optimal Stopping Problems for Matrix-Exponential Jump-Diffusion Processes

2012 ◽  
Vol 49 (02) ◽  
pp. 531-548
Author(s):  
Yuan-Chung Sheu ◽  
Ming-Yao Tsai
Keyword(s):  
Explicit Formula ◽  
Optimal Stopping ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Optimal Level ◽  
Matrix Exponential ◽  
Call Type ◽  
Jump Diffusion Processes ◽  
Averaging Problem ◽  
Optimal Stopping Problems

In this paper we consider optimal stopping problems for a general class of reward functions under matrix-exponential jump-diffusion processes. Given an American call-type reward function in this class, following the averaging problem approach (see, for example, Alili and Kyprianou (2005), Kyprianou and Surya (2005), Novikov and Shiryaev (2007), and Surya (2007)), we give an explicit formula for solutions of the corresponding averaging problem. Based on this explicit formula, we obtain the optimal level and the value function for American call-type optimal stopping problems.

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