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Sequential testing of a Wiener process with costly observations
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen, Tillämpad matematik och statistik.
(engelsk)Artikkel i tidsskrift (Annet vitenskapelig) Submitted
Abstract [en]

We consider the sequential testing of two simple hypotheses for the drift of a Brownian motion when each observation of the underlying process is associated with a positive cost. In this setting where continuous monitoring of the underlying process is not feasible, the question is not only whether to stop or to continue at a given observation time, but also, if continuing,how to distribute the next observation time. Adopting a Bayesian methodology, we show that the value function can be characterized as the unique fixed point of an associated operator, and that it can be constructed using an iterative scheme. Moreover, the optimal sequential distribution of observation times can be described in terms of the fixed point.

HSV kategori
Forskningsprogram
Matematik med inriktning mot tillämpad matematik
Identifikatorer
URN: urn:nbn:se:uu:diva-316571OAI: oai:DiVA.org:uu-316571DiVA, id: diva2:1078320
Tilgjengelig fra: 2017-03-03 Laget: 2017-03-03 Sist oppdatert: 2017-03-22
Inngår i avhandling
1. Valuation and Optimal Strategies in Markets Experiencing Shocks
Åpne denne publikasjonen i ny fane eller vindu >>Valuation and Optimal Strategies in Markets Experiencing Shocks
2017 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
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.

sted, utgiver, år, opplag, sider
Uppsala: Department of Mathematics, 2017. s. 30
Serie
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 100
Emneord
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
HSV kategori
Forskningsprogram
Matematik med inriktning mot tillämpad matematik
Identifikatorer
urn:nbn:se:uu:diva-316578 (URN)978-91-506-2625-4 (ISBN)
Disputas
2017-05-03, room 80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 10:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2017-04-11 Laget: 2017-03-14 Sist oppdatert: 2017-04-11

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