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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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:	Date Event 14 May 2014 Published 17 September 2013 Accepted August 2012 Submitted
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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