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Monotonicity of the value function for a two-dimensional optimal stopping problem

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Assing, Sigurd, Jacka, Saul D. and Ocejo, Adriana (2014) Monotonicity of the value function for a two-dimensional optimal stopping problem. The Annals of Applied Probability, 24 (4). pp. 1554-1584. doi:10.1214/13-AAP956 ISSN 1050-5164.

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Official URL: http://dx.doi.org/10.1214/13-AAP956

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Abstract

We consider a pair (X,Y) of stochastic processes satisfying the equation dX=a(X)YdB driven by a Brownian motion and study the monotonicity and continuity in y of the value function v(x,y)=sup τ E x,y [e −qτ g(X τ )] , 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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH): Optimal stopping (Mathematical statistics), Options (Finance) -- Mathematical models, Probabilities, Stochastic processes, Brownian motion processes, Stochastic models
Journal or Publication Title: The Annals of Applied Probability
Publisher: Institute of Mathematical Statistics
ISSN: 1050-5164
Official Date: 14 May 2014
Dates:
DateEvent
14 May 2014Published
17 September 2013Accepted
August 2012Submitted
Volume: 24
Number: 4
Page Range: pp. 1554-1584
DOI: 10.1214/13-AAP956
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 14 January 2016
Date of first compliant Open Access: 14 January 2016

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