uu.seUppsala University Publications

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Calibration, Optimality and Financial MathematicsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2013 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Department of Mathematics, 2013. , 25 p.
##### Series

Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 83
##### Keyword [en]

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: urn:nbn:se:uu:diva-209235ISBN: 978-91-506-2377-2 (print)OAI: oai:DiVA.org:uu-209235DiVA: diva2:656421
##### Public defence

2013-11-29, Ångström, rum 2001, Ångströmslaboratoriet , Lägerhyddsvägen 1, Uppsala, 10:15 (English)
##### Opponent

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##### Supervisors

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#####

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Available from: 2013-11-07 Created: 2013-10-15 Last updated: 2013-11-07
##### List of papers

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.

1. Recovering a piecewise constant volatility from perpetual put option prices$(function(){PrimeFaces.cw("OverlayPanel","overlay372123",{id:"formSmash:j_idt508:0:j_idt514",widgetVar:"overlay372123",target:"formSmash:j_idt508:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Optimal selling of an asset under incomplete information$(function(){PrimeFaces.cw("OverlayPanel","overlay385414",{id:"formSmash:j_idt508:1:j_idt514",widgetVar:"overlay385414",target:"formSmash:j_idt508:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Optimal selling of an asset with jumps under incomplete information$(function(){PrimeFaces.cw("OverlayPanel","overlay469103",{id:"formSmash:j_idt508:2:j_idt514",widgetVar:"overlay469103",target:"formSmash:j_idt508:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. The optimal dividend problem in the dual model$(function(){PrimeFaces.cw("OverlayPanel","overlay656289",{id:"formSmash:j_idt508:3:j_idt514",widgetVar:"overlay656289",target:"formSmash:j_idt508:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Short-time implied volatility in exponential Lévy models$(function(){PrimeFaces.cw("OverlayPanel","overlay656385",{id:"formSmash:j_idt508:4:j_idt514",widgetVar:"overlay656385",target:"formSmash:j_idt508:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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