Optimal Reinsurance Under Distortion Risk Measures and Expected Value Premium Principle for Reinsurer

This paper discusses optimal reinsurance strategy by minimizing insurer's risk under one general risk measure:Distortion risk measure.The authors assume that the reinsurance premium is determined by the expected value premium principle and the retained loss of the insurer is an increasing function of the initial loss.An explicit solution of the insurer's optimal reinsurance problem is obtained.The optimal strategies for some special distortion risk measures,such as value-at-risk(VaR) and tail value-at-risk(TVaR),are also investigated.

Optimal reinsurance designs based on risk measures:a review

Reinsurance is an effective way for an insurance company to control its risk.How to design an optimal reinsurance contract is not only a key topic in actuarial science,but also an interesting research question in mathematics and statistics.Optimal reinsurance design problems can be proposed from different perspectives.Risk measures as tools of quantitative risk management have been extensively used in insurance and finance.Optimal reinsurance designs based on risk measures have been widely studied in the literature of insurance and become an active research topic.Different research approaches have been developed and many interesting results have been obtained in this area.These approaches and results have potential applications in future research.In this article,we review the recent advances in optimal reinsurance designs based on risk measures in static models and discuss some interesting problems on this topic for future research.

Tail Distortion Risk Measure for Portfolio with Multivariate Regularly Variation

For the multiplicative background risk model,a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation.In this paper,we investigate the tail asymptotics of the portfolio loss ∑_(i=1)^(d)R_(i)S,where the stand-alone risk vector R=(R_(1),...,R_(d))follows a multivariate regular variation and is independent of the background risk factor S.An explicit asymptotic formula is established for the tail distortion risk measure,and an example is given to illustrate our obtained results.

Remarks on Equality of Two Distributions under Some Partial Orders

In this note we establish some appropriate conditions for stochastic equality of two random vari- ables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result are also considered.