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The optimal dividend problem in the dual model
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 46, no 3, 746-765 p.Article in journal (Refereed) Published
Abstract [en]

We study de Finetti's optimal dividend problem, also known as the optimal harvesting problem, in the dual model. In this model, the firm value is affected both by continuous fluctuations and by upward directed jumps. We use a fixed point method to show that the solution of the optimal dividend problem with jumps can be obtained as the limit of a sequence of stochastic control problems for a diffusion. In each problem, the optimal dividend strategy is of barrier type, and the rate of convergence of the barrier and the corresponding value function is exponential.

Place, publisher, year, edition, pages
2014. Vol. 46, no 3, 746-765 p.
Keyword [en]
Optimal distribution of dividends, de Finetti’s dividend problem, optimal harvesting, singular stochastic control, jump-diffusion model.
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-209219ISI: 000341280200008OAI: oai:DiVA.org:uu-209219DiVA: diva2:656289
Available from: 2013-10-15 Created: 2013-10-15 Last updated: 2017-12-06Bibliographically approved
In thesis
1. 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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