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dc.contributor.advisorYang, Wei-Shih
dc.creatorXiong, Sheng
dc.date.accessioned2020-11-05T16:15:47Z
dc.date.available2020-11-05T16:15:47Z
dc.date.issued2011
dc.identifier.other864885292
dc.identifier.urihttp://hdl.handle.net/20.500.12613/3866
dc.description.abstractIn this dissertation, we have studied diffusion models and their applications in risk theory and insurance. Let Xt be a d-dimensional diffusion process satisfying a system of Stochastic Differential Equations defined on an open set G Rd, and let Ut be a utility function of Xt with U0 = u0. Let T be the first time that Ut reaches a level u^*. We study the Laplace transform of the distribution of T, as well as the probability of ruin, psileft(u_{0}right)=Prleft{ T<inftyright} , and other important probabilities. A class of exponential martingales is constructed to analyze the asymptotic properties of all probabilities. In addition, we prove that the expected discounted penalty function, a generalization of the probability of ultimate ruin, satisfies an elliptic partial differential equation, subject to some initial boundary conditions. Two examples from areas of actuarial work to which martingales have been applied are given to illustrate our methods and results: 1. Insurer's insolvency. 2. Terrorism risk. In particular, we study insurer's insolvency for the Cram'{e}r-Lundberg model with investments whose price follows a geometric Brownian motion. We prove the conjecture proposed by Constantinescu and Thommann.
dc.format.extent76 pages
dc.language.isoeng
dc.publisherTemple University. Libraries
dc.relation.ispartofTheses and Dissertations
dc.rightsIN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectMathematics
dc.subjectMartingale
dc.subjectRuin Theory
dc.subjectStochastic Differential Equation
dc.subjectTerrorism Risk
dc.titleStochastic Differential Equations: Some Risk and Insurance Applications
dc.typeText
dc.type.genreThesis/Dissertation
dc.contributor.committeememberPowers, Michael R.
dc.contributor.committeememberChen, Hua
dc.contributor.committeememberBerhanu, Shiferaw
dc.description.departmentMathematics
dc.relation.doihttp://dx.doi.org/10.34944/dspace/3848
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.description.degreePh.D.
refterms.dateFOA2020-11-05T16:15:47Z


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