uu.seUppsala universitets publikasjoner
Endre søk
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Optimal Sequential Decisions in Hidden-State Models
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Matematiska institutionen.
2017 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Fritextbeskrivning
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 [en]
sequential analysis, optimal stopping, optimal liquidation, drift uncertainty, incomplete information, stochastic filtering
HSV kategori
Identifikatorer
URN: urn:nbn:se:uu:diva-320809ISBN: 978-91-506-2641-4 (tryckt)OAI: oai:DiVA.org:uu-320809DiVA, id: diva2:1091116
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
Delarbeid
1. Optimal liquidation of an asset under drift uncertainty
Åpne denne publikasjonen i ny fane eller vindu >>Optimal liquidation of an asset under drift uncertainty
2016 (engelsk)Inngår i: SIAM Journal on Financial Mathematics, ISSN 1945-497X, E-ISSN 1945-497XArtikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift by allowing an arbitrary probability distribution to characterize the uncertainty about the drift parameter. Filtering theory is used to describe the evolution of the posterior beliefs about the drift once the price process is being observed. An optimal stopping time is determined as the first passage time of the posterior mean below a monotone boundary, which can be characterized as the unique solution to a nonlinear integral equation. We also study monotonicity properties with respect to the prior distribution and the asset volatility.

Emneord
optimal liquidation, incomplete information, sequential analysis
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-283523 (URN)10.1137/15M1033265 (DOI)000391850000013 ()
Tilgjengelig fra: 2016-04-13 Laget: 2016-04-13 Sist oppdatert: 2017-11-30bibliografisk kontrollert
2. Asset liquidation under drift uncertainty and regime-switching volatility
Åpne denne publikasjonen i ny fane eller vindu >>Asset liquidation under drift uncertainty and regime-switching volatility
(engelsk)Artikkel i tidsskrift (Annet vitenskapelig) Submitted
Abstract [en]

Optimal liquidation of an asset with unknown constant drift and stochastic regime-switching volatility is studied. The uncertainty about the drift is represented by an arbitrary probability distribution, the stochastic volatility is modelled by m-state Markov chain. Using filtering theory, an equivalent reformulation of the original problem as a four-dimensional optimal stopping problem is found and then analysed by constructing approximating sequences of three-dimensional optimal stopping problems. An optimal liquidation strategy and various structural properties of the problem are determined. Analysis of the two-point prior case is presented in detail, building on which, an outline of the extension to the general prior case is given.

Emneord
optimal liquidation, model uncertainty, regime-switching volatility, sequential analysis
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-320805 (URN)
Tilgjengelig fra: 2017-04-25 Laget: 2017-04-25 Sist oppdatert: 2017-04-26
3. Bayesian Sequential Testing Of The Drift Of A Brownian Motion
Åpne denne publikasjonen i ny fane eller vindu >>Bayesian Sequential Testing Of The Drift Of A Brownian Motion
2015 (engelsk)Inngår i: ESAIM. P&S, ISSN 1292-8100, E-ISSN 1262-3318, Vol. 19, s. 626-648Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We study a classical Bayesian statistics 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 for general prior distributions. The statistical problem is reformulated as an optimal stopping problem with the current conditional probability that the drift is non-negative as the underlying process. The volatility of this conditional probability process is shown to be non-increasing in time, which enables us to prove monotonicity and continuity of the optimal stopping boundaries as well as to characterize them completely in the finite-horizon case as the unique continuous solution to a pair of integral equations. In the infinite-horizon case, the boundaries are shown to solve another pair of integral equations and a convergent approximation scheme for the boundaries is provided. Also, we describe the dependence between the prior distribution and the long-term asymptotic behaviour of the boundaries.

Emneord
Bayesian analysis, sequential hypothesis testing, optimal stopping
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-276901 (URN)10.1051/ps/2015012 (DOI)000368218600031 ()
Forskningsfinansiär
Swedish Research Council
Tilgjengelig fra: 2016-02-16 Laget: 2016-02-16 Sist oppdatert: 2017-11-30bibliografisk kontrollert
4. Optimal stopping of a Brownian bridge with an unknown pinning point
Åpne denne publikasjonen i ny fane eller vindu >>Optimal stopping of a Brownian bridge with an unknown pinning point
(engelsk)Artikkel i tidsskrift (Annet vitenskapelig) Submitted
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-320806 (URN)
Tilgjengelig fra: 2017-04-25 Laget: 2017-04-25 Sist oppdatert: 2017-04-26
5. Wiener disorder detection under disorder magnitude uncertainty
Åpne denne publikasjonen i ny fane eller vindu >>Wiener disorder detection under disorder magnitude uncertainty
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
HSV kategori
Identifikatorer
urn:nbn:se:uu:diva-320807 (URN)
Tilgjengelig fra: 2017-04-25 Laget: 2017-04-25 Sist oppdatert: 2017-04-26

Open Access i DiVA

fulltext(3529 kB)189 nedlastinger
Filinformasjon
Fil FULLTEXT01.pdfFilstørrelse 3529 kBChecksum SHA-512
1317aac6932f48eb4433dc1a5df9739d1c741d175f4a46a01ab32f2603fb7f3fe51b965a4553e7e51a39c82bc7a0c49f6c78db9520c75ef0e6219c9c5c95e3fc
Type fulltextMimetype application/pdf

Personposter BETA

Vaicenavicius, Juozas

Søk i DiVA

Av forfatter/redaktør
Vaicenavicius, Juozas
Av organisasjonen

Søk utenfor DiVA

GoogleGoogle Scholar
Totalt: 189 nedlastinger
Antall nedlastinger er summen av alle nedlastinger av alle fulltekster. Det kan for eksempel være tidligere versjoner som er ikke lenger tilgjengelige

isbn
urn-nbn

Altmetric

isbn
urn-nbn
Totalt: 1436 treff
RefereraExporteraLink to record
Permanent link

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