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Optimal selling of an asset under incomplete information
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2011 (English)In: International Journal of Stochastic Analysis, ISSN 2090-3332, E-ISSN 2090-3340, Vol. 2011, 543590- p.Article in journal (Refereed) Published
Abstract [en]

We consider an agent who wants to liquidate an asset with unknown drift. The agent believes that the drift takes one of two given values and has initially an estimate for the probability of either of them. As time goes by, the agent observes the asset price and can thereforeupdate his beliefs about the probabilities for the drift distribution. We formulate an optimal stopping problem that describes the liquidation problem, and we demonstrate that the optimal strategy is to liquidate the first time the asset price falls below a certain time-dependent boundary. Moreover, this boundary is shown to be monotonically increasing, continuous and to satisfy a nonlinear integral equation.

Place, publisher, year, edition, pages
2011. Vol. 2011, 543590- p.
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-141329DOI: 10.1155/2011/543590OAI: oai:DiVA.org:uu-141329DiVA: diva2:385414
Available from: 2011-01-11 Created: 2011-01-11 Last updated: 2017-12-11Bibliographically approved
In thesis
1. Optimal stopping and incomplete information in finance
Open this publication in new window or tab >>Optimal stopping and incomplete information in finance
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2011. 45 p.
Series
U.U.D.M. report / Uppsala University, Department of Mathematics, ISSN 1101-3591 ; 2011:24
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-164340 (URN)
Presentation
2012-01-17, 13:15 (English)
Supervisors
Available from: 2011-12-22 Created: 2011-12-19 Last updated: 2011-12-22Bibliographically approved
2. Calibration, Optimality and Financial Mathematics
Open this publication in new window or tab >>Calibration, Optimality and Financial Mathematics
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of a summary and five papers, dealing with financial applications of optimal stopping, optimal control and volatility.

In Paper I, we present a method to recover a time-independent piecewise constant volatility from a finite set of perpetual American put option prices.

In Paper II, we study the optimal liquidation problem under the assumption that the asset price follows a geometric Brownian motion with unknown drift, which takes one of two given values. The optimal strategy is to liquidate the first time the asset price falls below a monotonically increasing, continuous time-dependent boundary.

In Paper III, we investigate the optimal liquidation problem under the assumption that the asset price follows a jump-diffusion with unknown intensity, which takes one of two given values. The best liquidation strategy is to sell the asset the first time the jump process falls below or goes above a monotone time-dependent boundary.

Paper IV treats the optimal dividend problem in a model allowing for positive jumps of the underlying firm value. The optimal dividend strategy is of barrier type, i.e. to pay out all surplus above a certain level as dividends, and then pay nothing as long as the firm value is below this level.

Finally, in Paper V it is shown that a necessary and sufficient condition for the explosion of implied volatility near expiry in exponential Lévy models is the existence of jumps towards the strike price in the underlying process.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2013. 25 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 83
Keyword
perpetual put option, calibration of models, piecewise constant volatility, optimal liquidation of an asset, incomplete information, optimal stopping, jump-diffusion model, optimal distribution of dividends, singular stochastic control, implied volatility, exponential Lévy models, short-time asymptotic behavior.
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-209235 (URN)978-91-506-2377-2 (ISBN)
Public defence
2013-11-29, Ångström, rum 2001, Ångströmslaboratoriet , Lägerhyddsvägen 1, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2013-11-07 Created: 2013-10-15 Last updated: 2013-11-07

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Ekström, ErikLu, Bing

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