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Optimal stopping and incomplete information in finance
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
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: urn:nbn:se:uu:diva-164340OAI: oai:DiVA.org:uu-164340DiVA: diva2:467439
Presentation
2012-01-17, 13:15 (English)
Supervisors
Available from: 2011-12-22 Created: 2011-12-19 Last updated: 2011-12-22Bibliographically approved
List of papers
1. Recovering a piecewise constant volatility from perpetual put option prices
Open this publication in new window or tab >>Recovering a piecewise constant volatility from perpetual put option prices
2010 (English)In: Journal of Applied Probability, ISSN 0021-9002, E-ISSN 1475-6072, Vol. 47, no 3, 680-692 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we present a method to recover a time-homogeneous piecewise constant volatility from a finite set of perpetual put option prices. The whole calculation process of the volatility is decomposed into easy computations in many fixed disjoint intervals. In each interval, the volatility is obtained by solving a system of nonlinear equations.

Keyword
Perpetual put option, calibration of models, piecewise constant volatility
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-134147 (URN)10.1239/jap/1285335403 (DOI)000282856000005 ()
Available from: 2010-11-24 Created: 2010-11-22 Last updated: 2017-12-12Bibliographically approved
2. Optimal selling of an asset under incomplete information
Open this publication in new window or tab >>Optimal selling of an asset under incomplete information
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.

National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-141329 (URN)10.1155/2011/543590 (DOI)
Available from: 2011-01-11 Created: 2011-01-11 Last updated: 2017-12-11Bibliographically approved
3. Optimal selling of an asset with jumps under incomplete information
Open this publication in new window or tab >>Optimal selling of an asset with jumps under incomplete information
2013 (English)In: Applied Mathematical Finance, ISSN 1350-486X, E-ISSN 1433-4313, Vol. 20, no 6, 599-610 p.Article in journal (Refereed) Published
Abstract [en]

We study the optimal liquidation strategy of an asset with price process satisfying a jump diffusion model with unknown jump intensity. It is assumed that the intensity takes one of two given values, and we have an initial estimate for the probability of both of them. As time goes by, by observing the price fluctuations, we can thus update our beliefs about the probabilities for the intensity distribution. We formulate an optimal stopping problem describing the optimal liquidation problem. It is shown that the optimal strategy is to liquidate the first time the point process falls below (goes above) a certain time-dependent boundary.

National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-164690 (URN)10.1080/1350486X.2013.810462 (DOI)
Available from: 2011-12-22 Created: 2011-12-22 Last updated: 2017-12-08Bibliographically approved

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Citation style
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  • Other locale
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Output format
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