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postgraduate thesis: Some topics in risk theory and optimal capital allocation problems

TitleSome topics in risk theory and optimal capital allocation problems
Authors
Advisors
Advisor(s):Cheung, KC
Issue Date2012
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Liu, B. [刘彬彬]. (2012). Some topics in risk theory and optimal capital allocation problems. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4819929
AbstractIn recent years, the Markov Regime-Switching model and the class of Archimedean copulas have been widely applied to a variety of finance-related fields. The Markov Regime-Switching model can reflect the reality that the underlying economy is changing over time. Archimedean copulas are one of the most popular classes of copulas because they have closed form expressions and have great flexibility in modeling different kinds of dependencies. In the thesis, we first consider a discrete-time risk process based on the compound binomial model with regime-switching. Some general recursive formulas of the expected penalty function have been obtained. The orderings of ruin probabilities are investigated. In particular, we show that if there exists a stochastic dominance relationship between random claims at different regimes, then we can order ruin probabilities under different initial regimes. Regarding capital allocation problems, which are important areas in finance and risk management, this thesis studies the problems of optimal allocation of policy limits and deductibles when the dependence structure among risks is modeled by an Archimedean copula. By employing the concept of arrangement increasing and stochastic dominance, useful qualitative results of the optimal allocations are obtained. Then we turn our attention to a new family of risk measures satisfying a set of proposed axioms, which includes the class of distortion risk measures with concave distortion functions. By minimizing the new risk measures, we consider the optimal allocation of policy limits and deductibles problems based on the assumption that for each risk there exists an indicator random variable which determines whether the risk occurs or not. Several sufficient conditions to order the optimal allocations are obtained using tools in stochastic dominance theory.
DegreeDoctor of Philosophy
SubjectRisk management - Mathematical models.
Investments - Mathematical models
Portfolio management - Mathematical models.
Dept/ProgramStatistics and Actuarial Science

 

DC FieldValueLanguage
dc.contributor.advisorCheung, KC-
dc.contributor.authorLiu, Binbin-
dc.contributor.author刘彬彬-
dc.date.issued2012-
dc.identifier.citationLiu, B. [刘彬彬]. (2012). Some topics in risk theory and optimal capital allocation problems. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4819929-
dc.description.abstractIn recent years, the Markov Regime-Switching model and the class of Archimedean copulas have been widely applied to a variety of finance-related fields. The Markov Regime-Switching model can reflect the reality that the underlying economy is changing over time. Archimedean copulas are one of the most popular classes of copulas because they have closed form expressions and have great flexibility in modeling different kinds of dependencies. In the thesis, we first consider a discrete-time risk process based on the compound binomial model with regime-switching. Some general recursive formulas of the expected penalty function have been obtained. The orderings of ruin probabilities are investigated. In particular, we show that if there exists a stochastic dominance relationship between random claims at different regimes, then we can order ruin probabilities under different initial regimes. Regarding capital allocation problems, which are important areas in finance and risk management, this thesis studies the problems of optimal allocation of policy limits and deductibles when the dependence structure among risks is modeled by an Archimedean copula. By employing the concept of arrangement increasing and stochastic dominance, useful qualitative results of the optimal allocations are obtained. Then we turn our attention to a new family of risk measures satisfying a set of proposed axioms, which includes the class of distortion risk measures with concave distortion functions. By minimizing the new risk measures, we consider the optimal allocation of policy limits and deductibles problems based on the assumption that for each risk there exists an indicator random variable which determines whether the risk occurs or not. Several sufficient conditions to order the optimal allocations are obtained using tools in stochastic dominance theory.-
dc.languageeng-
dc.publisherThe University of Hong Kong (Pokfulam, Hong Kong)-
dc.relation.ispartofHKU Theses Online (HKUTO)-
dc.rightsThe author retains all proprietary rights, (such as patent rights) and the right to use in future works.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.source.urihttp://hub.hku.hk/bib/B48199291-
dc.subject.lcshRisk management - Mathematical models.-
dc.subject.lcshInvestments - Mathematical models-
dc.subject.lcshPortfolio management - Mathematical models.-
dc.titleSome topics in risk theory and optimal capital allocation problems-
dc.typePG_Thesis-
dc.identifier.hkulb4819929-
dc.description.thesisnameDoctor of Philosophy-
dc.description.thesislevelDoctoral-
dc.description.thesisdisciplineStatistics and Actuarial Science-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.5353/th_b4819929-
dc.date.hkucongregation2012-

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