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dc.contributor.authorwang ying 16:55:19 (GMT) 16:55:19 (GMT)
dc.description.abstractRisk measures (or premium principles) and capital allocation principles play a signi cant role in risk management. Regulators and companies in the nancial markets usually adopt an appropriate risk measure, for example, Value-at-Risk (VaR) or Tail Value-at-Risk (TVaR), to determine the benchmarks. However, these risk measures are determined from the loss functions with constant weights, not random weight functions. This thesis proposes new approaches to determine risk measures from two perspectives. Firstly, we will generalize the de nition of the tail subadditivity for distortion risk measures; we de ne the generalized GlueVaR (a linear combination of VaR and TVaRs) to approach any coherent distortion risk measure. Secondly, we will research the risk measures (or premium principles) and capital allocation principles based on the loss functions with random weight functions. The new reinsurance premium principles are derived similarly to the new risk measures. The two thresholds for the weight in the loss function can be employed by reinsurance companies as benchmarks when pricing the reinsurance products. The capital allocation principles derived based on the weighted loss functions are both mathematically and economically reasonable. Many of the risk measures and allocation principles, including the new risk measures, can be covered by this model. The results of this thesis have not only uni ed many of the risk measures and capital allocation principles, but also provided new and practical models.en
dc.publisherUniversity of Waterlooen
dc.subjectrisk measureen
dc.subjectcapital allocation principleen
dc.subjectweighted quantilesen
dc.subjecttail sub-additiveen
dc.subjectdistortion risk measureen
dc.subjectweighted VaRen
dc.subjectweighted expectilesen
dc.subjectcapital deficit risken
dc.subjectcapital surplus risken
dc.subjectadd on and offen
dc.subjectoptimal reinsuranceen
dc.subjectreinsurance premiumen
dc.titleRisk Measures and Capital Allocation Principles for Risk Managementen
dc.typeDoctoral Thesisen
dc.pendingfalse and Actuarial Scienceen Scienceen of Waterlooen
uws-etd.degreeDoctor of Philosophyen
uws.contributor.advisorCai, Jun
uws.contributor.affiliation1Faculty of Mathematicsen

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