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Optimal stopping games for a process with jumps
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
(English)Article in journal (Other academic) Submitted
Abstract [en]

This paper presents a study of a general two-player optimal stopping game in a jump-diffusion model. An iterative scheme to find the value of this game is derived, specifically the value is shown to be the limit of a sequence of stopping games for a related diffusion but with a running reward. Furthermore the convergence is uniform and exponential. The special case of a cancellable put option is studied.

National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-316577OAI: oai:DiVA.org:uu-316577DiVA: diva2:1078317
Available from: 2017-03-03 Created: 2017-03-03 Last updated: 2017-03-14
In thesis
1. Valuation and Optimal Strategies in Markets Experiencing Shocks
Open this publication in new window or tab >>Valuation and Optimal Strategies in Markets Experiencing Shocks
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis treats a range of stochastic methods with various applications, most notably in finance. It is comprised of five articles, and a summary of the key concepts and results these are built on.

The first two papers consider a jump-to-default model, which is a model where some quantity, e.g. the price of a financial asset, is represented by a stochastic process which has continuous sample paths except for the possibility of a sudden drop to zero. In Paper I prices of European-type options in this model are studied together with the partial integro-differential equation that characterizes the price. In Paper II the price of a perpetual American put option in the same model is found in terms of explicit formulas. Both papers also study the parameter monotonicity and convexity properties of the option prices.

The third and fourth articles both deal with valuation problems in a jump-diffusion model. Paper III concerns the optimal level at which to exercise an American put option with finite time horizon. More specifically, the integral equation that characterizes the optimal boundary is studied. In Paper IV we consider a stochastic game between two players and determine the optimal value and exercise strategy using an iterative technique.

Paper V employs a similar iterative method to solve the statistical problem of determining the unknown drift of a stochastic process, where not only running time but also each observation of the process is costly.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2017. 30 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 100
Keyword
American options, optimal stopping, game options, jump diffusion, jump to default, free-boundary problems, early exercise premium, integral equation, parabolic pde, convexity, sequential testing, fixed-point approach
National Category
Probability Theory and Statistics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
urn:nbn:se:uu:diva-316578 (URN)978-91-506-2625-4 (ISBN)
Public defence
2017-05-03, room 80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2017-04-11 Created: 2017-03-14 Last updated: 2017-04-11

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