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August 2014 Monotonicity of the value function for a two-dimensional optimal stopping problem
Sigurd Assing, Saul Jacka, Adriana Ocejo
Ann. Appl. Probab. 24(4): 1554-1584 (August 2014). DOI: 10.1214/13-AAP956


We consider a pair $(X,Y)$ of stochastic processes satisfying the equation $dX=a(X)Y\,dB$ driven by a Brownian motion and study the monotonicity and continuity in $y$ of the value function $v(x,y)=\sup_{\tau}E_{x,y}[e^{-q\tau}g(X_{\tau})]$, where the supremum is taken over stopping times with respect to the filtration generated by $(X,Y)$. Our results can successfully be applied to pricing American options where $X$ is the discounted price of an asset while $Y$ is given by a stochastic volatility model such as those proposed by Heston or Hull and White. The main method of proof is based on time-change and coupling.


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Sigurd Assing. Saul Jacka. Adriana Ocejo. "Monotonicity of the value function for a two-dimensional optimal stopping problem." Ann. Appl. Probab. 24 (4) 1554 - 1584, August 2014.


Published: August 2014
First available in Project Euclid: 14 May 2014

zbMATH: 1316.60056
MathSciNet: MR3211004
Digital Object Identifier: 10.1214/13-AAP956

Primary: 60G40
Secondary: 91G20

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.24 • No. 4 • August 2014
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