Optimal stopping problem for jump–diffusion processes with regime-switching

2021 ◽  
Vol 41 ◽  
pp. 101029
Author(s):  
Jinghai Shao ◽  
Taoran Tian
Keyword(s):  
Optimal Stopping ◽  
Regime Switching ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Optimal Stopping Problem ◽  
Jump Diffusion Processes

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 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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