uu.seUppsala universitets publikationer
Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
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.
(Engelska)Artikel i tidskrift (Övrigt vetenskapligt) Submitted
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
URN: urn:nbn:se:uu:diva-320806OAI: oai:DiVA.org:uu-320806DiVA, id: diva2:1091112
Tillgänglig från: 2017-04-25 Skapad: 2017-04-25 Senast uppdaterad: 2017-04-26
Ingår i avhandling
1. Optimal Sequential Decisions in Hidden-State Models
Öppna denna publikation i ny flik eller fönster >>Optimal Sequential Decisions in Hidden-State Models
2017 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Uppsala: Department of Mathematics, Uppsala University, 2017. s. 26
Serie
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 101
Nyckelord
sequential analysis, optimal stopping, optimal liquidation, drift uncertainty, incomplete information, stochastic filtering
Nationell ämneskategori
Sannolikhetsteori och statistik
Identifikatorer
urn:nbn:se:uu:diva-320809 (URN)978-91-506-2641-4 (ISBN)
Disputation
2017-06-09, 80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:00 (Engelska)
Opponent
Handledare
Tillgänglig från: 2017-05-18 Skapad: 2017-04-26 Senast uppdaterad: 2017-05-18

Open Access i DiVA

Fulltext saknas i DiVA

Sök vidare i DiVA

Av författaren/redaktören
Vaicenavicius, Juozas
Av organisationen
Tillämpad matematik och statistik
Sannolikhetsteori och statistik

Sök vidare utanför DiVA

GoogleGoogle Scholar

urn-nbn

Altmetricpoäng

urn-nbn
Totalt: 244 träffar
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf