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Valuation and Optimal Strategies in Markets Experiencing ShocksPrimeFaces.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}); 2017 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Description

##### Abstract [en]

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

Uppsala: Department of Mathematics , 2017. , 30 p.
##### Series

Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 100
##### Keyword [en]

American options, optimal stopping, game options, jump diffusion, jump to default, free-boundary problems, early exercise premium, integral equation, parabolic pde, convexity, sequential testing, fixed-point approach
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics with specialization in Applied Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-316578ISBN: 978-91-506-2625-4 (print)OAI: oai:DiVA.org:uu-316578DiVA: diva2:1081367
##### Public defence

2017-05-03, room 80101, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 10:15 (English)
##### Opponent

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#####

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Available from: 2017-04-11 Created: 2017-03-14 Last updated: 2017-04-11
##### List of papers

This thesis treats a range of stochastic methods with various applications, most notably in finance. It is comprised of five articles, and a summary of the key concepts and results these are built on.

The first two papers consider a jump-to-default model, which is a model where some quantity, e.g. the price of a financial asset, is represented by a stochastic process which has continuous sample paths except for the possibility of a sudden drop to zero. In Paper I prices of European-type options in this model are studied together with the partial integro-differential equation that characterizes the price. In Paper II the price of a perpetual American put option in the same model is found in terms of explicit formulas. Both papers also study the parameter monotonicity and convexity properties of the option prices.

The third and fourth articles both deal with valuation problems in a jump-diffusion model. Paper III concerns the optimal level at which to exercise an American put option with finite time horizon. More specifically, the integral equation that characterizes the optimal boundary is studied. In Paper IV we consider a stochastic game between two players and determine the optimal value and exercise strategy using an iterative technique.

Paper V employs a similar iterative method to solve the statistical problem of determining the unknown drift of a stochastic process, where not only running time but also each observation of the process is costly.

1. Pricing equations in jump-to-default models$(function(){PrimeFaces.cw("OverlayPanel","overlay1066802",{id:"formSmash:j_idt481:0:j_idt485",widgetVar:"overlay1066802",target:"formSmash:j_idt481:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. The perpetual American put option in jump-to-default models$(function(){PrimeFaces.cw("OverlayPanel","overlay1066800",{id:"formSmash:j_idt481:1:j_idt485",widgetVar:"overlay1066800",target:"formSmash:j_idt481:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. The integral equation for the American put boundary in models with jumps$(function(){PrimeFaces.cw("OverlayPanel","overlay1078315",{id:"formSmash:j_idt481:2:j_idt485",widgetVar:"overlay1078315",target:"formSmash:j_idt481:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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5. Sequential testing of a Wiener process with costly observations$(function(){PrimeFaces.cw("OverlayPanel","overlay1078320",{id:"formSmash:j_idt481:4:j_idt485",widgetVar:"overlay1078320",target:"formSmash:j_idt481:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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