Risk Measures and Capital Allocation Principles for Risk Management
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Date
2016-09-21
Authors
wang ying
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Risk 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.
Description
Keywords
risk measure, capital allocation principle, weighted quantiles, tail sub-additive, distortion risk measure, weighted VaR, weighted expectiles, capital deficit risk, capital surplus risk, add on and off, optimal reinsurance, reinsurance premium