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