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Optimal stopping of a Brownian bridge with an unknown pinning point
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
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Identifikatorer
URN: urn:nbn:se:uu:diva-320806OAI: oai:DiVA.org:uu-320806DiVA, id: diva2:1091112
Tilgjengelig fra: 2017-04-25 Laget: 2017-04-25 Sist oppdatert: 2017-04-26
Inngår i avhandling
1. Optimal Sequential Decisions in Hidden-State Models
Åpne denne publikasjonen i ny fane eller vindu >>Optimal Sequential Decisions in Hidden-State Models
2017 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This doctoral thesis consists of five research articles on the general topic of optimal decision making under uncertainty in a Bayesian framework. The papers are preceded by three introductory chapters.

Papers I and II are dedicated to the problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. In Paper I, the price is modelled by the classical Black-Scholes model with unknown drift. The first passage time of the posterior mean below a monotone boundary is shown to be optimal. The boundary is characterised as the unique solution to a nonlinear integral equation. Paper II solves the same optimal liquidation problem, but in a more general model with stochastic regime-switching volatility. An optimal liquidation strategy and various structural properties of the problem are determined.

In Paper III, the problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the 0-1 loss function and a constant cost of observation per unit of time is studied from a Bayesian perspective. Optimal decision strategies for arbitrary prior distributions are determined and investigated. The strategies consist of two monotone stopping boundaries, which we characterise in terms of integral equations.

In Paper IV, the problem of stopping a Brownian bridge with an unknown pinning point to maximise the expected value at the stopping time is studied. Besides a few general properties established, structural properties of an optimal strategy are shown to be sensitive to the prior. A general condition for a one-sided optimal stopping region is provided.

Paper V deals with the problem of detecting a drift change of a Brownian motion under various extensions of the classical Wiener disorder problem. Monotonicity properties of the solution with respect to various model parameters are studied. Also, effects of a possible misspecification of the underlying model are explored.

sted, utgiver, år, opplag, sider
Uppsala: Department of Mathematics, Uppsala University, 2017. s. 26
Serie
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 101
Emneord
sequential analysis, optimal stopping, optimal liquidation, drift uncertainty, incomplete information, stochastic filtering
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-320809 (URN)978-91-506-2641-4 (ISBN)
Disputas
2017-06-09, 80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:00 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2017-05-18 Laget: 2017-04-26 Sist oppdatert: 2017-05-18

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