Probabilities of Ruin in Economics and Insurance under Light- and Heavy-tailed Distributions

Persistent Link:
http://hdl.handle.net/10150/556962
Title:
Probabilities of Ruin in Economics and Insurance under Light- and Heavy-tailed Distributions
Author:
Kim, Hyeonju
Issue Date:
2015
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This research is conducted on ruin problems in two fields. First, the ruin or survival of an economic agent over finite and infinite time horizons is explored for a one-good economy. A recursive relation derived for the intractable ruin distribution is used to compute its moments. A new system of Chebyshev inequalities, using an optimal allocation of different orders of moments over different ranges of the initial stock, provide good conservative estimates of the true ruin distribution. The second part of the research is devoted to the study of ruin probabilities in the general renewal model of insurance under both light- and heavy-tailed claim size distributions. Recent results on the dual problem of equilibrium of the Lindley-Spitzer Markov process provide clues to the orders of magnitude of finite time ruin probabilities in insurance. Extensive empirical studies show the disparity between the performances of light and heavy-tailed theoretical asymptotics vis-a-vis actual probabilities in finite time and/or with finite initial assets.
Type:
text; Electronic Dissertation
Keywords:
Statistics
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Statistics
Degree Grantor:
University of Arizona
Advisor:
Bhattacharya, Rabindra N.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleProbabilities of Ruin in Economics and Insurance under Light- and Heavy-tailed Distributionsen_US
dc.creatorKim, Hyeonjuen
dc.contributor.authorKim, Hyeonjuen
dc.date.issued2015en
dc.publisherThe University of Arizona.en
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en
dc.description.abstractThis research is conducted on ruin problems in two fields. First, the ruin or survival of an economic agent over finite and infinite time horizons is explored for a one-good economy. A recursive relation derived for the intractable ruin distribution is used to compute its moments. A new system of Chebyshev inequalities, using an optimal allocation of different orders of moments over different ranges of the initial stock, provide good conservative estimates of the true ruin distribution. The second part of the research is devoted to the study of ruin probabilities in the general renewal model of insurance under both light- and heavy-tailed claim size distributions. Recent results on the dual problem of equilibrium of the Lindley-Spitzer Markov process provide clues to the orders of magnitude of finite time ruin probabilities in insurance. Extensive empirical studies show the disparity between the performances of light and heavy-tailed theoretical asymptotics vis-a-vis actual probabilities in finite time and/or with finite initial assets.en
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectStatisticsen
thesis.degree.namePh.D.en
thesis.degree.leveldoctoralen
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineStatisticsen
thesis.degree.grantorUniversity of Arizonaen
dc.contributor.advisorBhattacharya, Rabindra N.en
dc.contributor.committeememberBhattacharya, Rabindra N.en
dc.contributor.committeememberLamoureux, Christopher G.en
dc.contributor.committeememberSethuraman, Sunderen
dc.contributor.committeememberWatkins, Joseph C.en
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