Hobson, David (David G.) and Klimmek, Martin. (2011) Constructing time-homogeneous generalized diffusions consistent with optimal stopping values. Stochastics An International Journal of Probability and Stochastic Processes, Vol.83 (No.4-6). pp. 477-503. ISSN 1744-2508

PDF WRAP_Hobson_1005.0160v1.pdf - Submitted Version Restricted to Repository staff only until 11 April 2013. - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (1682Kb)

Abstract

Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the problem value in this setting. In this article we consider an inverse problem; given the set of problem values for a family of objective functions, we aim to recover the diffusion. Under a natural assumption on the family of objective functions, we can characterize the existence and uniqueness of a diffusion for which the optimal stopping problems have the specified values. The solution of the problem relies on techniques from generalized convexity theory.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Optimal stopping (Mathematical statistics), Diffusion processes
Journal or Publication Title:	Stochastics An International Journal of Probability and Stochastic Processes
Publisher:	Taylor & Francis Ltd.
ISSN:	1744-2508
Date:	2011
Volume:	Vol.83
Number:	No.4-6
Page Range:	pp. 477-503
Identification Number:	10.1080/17442508.2010.522237
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
References:	[1] A. Alfonsi and B. Jourdain. General duality for perpetual American options. International Journal of Theoretical and Applied Finance, 11(6):545{566, 2008. [2] A. Alfonsi and B. Jourdain. Exact volatility calibration based on a Dupire-type call-put duality for perpetual American options. Nonlinear Differ. Equa. Appl, 16(4):523{554, 2009. [3] A.N. Borodin and P. Salminen. Handbook of Brownian Motion - Facts and Formulae. Birkhauser, 2nd edition, 2002. [4] G. Carlier. Duality and existence for a class of mass transportation problems and economic applications. Adv. in Mathematical economy, 5:1{22, 2003. [5] H. Dym and H.P. McKean. Gaussian Processes, Function Theory, and the Inverse Spectral Problem. Academic Press, Inc., 1976. [6] E. Ekstrom and D. Hobson. Recovering a time-homogeneous stock price process from perpetual option prices. Preprint, 2009. http://arxiv.org/abs/0903.4833. [7] W. Feller. The birth and death processes as diffusion processes. J. Math. Pures Appl., 38:301{345, 1959. [8] K. It^o and H.P McKean. Diffusion Processes and their Sample Paths. Springer-Verlag, 1974. [9] I.S. Kac. Pathological Birth-and-Death Processes and the Spectral Theory of Strings. Functional Analysis and Its Applications, 39(2):144{147, 2005. [10] S. Kotani and S. Watanabe. Krein's spectral theory of strings and generalized diffusion processes. Functional Analysis in Markov Processes, (ed. M. Fukushima), Lecture Notes in Math., 923:235{259, 1982. [11] S.T Rachev and L. Ruschendorf. Mass Transportation Problems, volume 1. Springer-Verlag, 1998. [12] R.T. Rockafellar. Convex Analysis. Princeton University Press, 1970. [13] L.C.G. Rogers and D. Williams. Diffusions, Markov Processes and Martingales, volume 2. Cambridge University Press, 2000. [14] C. Villani. Optimal Transport: Old and New. Springer-Verlag, 2009.
URI:	http://wrap.warwick.ac.uk/id/eprint/41080

Request changes to a record

Actions (login required)

View Item