Two Sufficient Conditions for Convex Ordering on Risk Aggregation

In this paper, we study two classes of optimal reinsurance models from perspectives of both insurers and reinsurers by minimizing their convex combination where the risk is measured by a distortion risk measure and the premium is given by a distortion premium principle. Firstly, we show that how optimal reinsurance models for the unconstrained optimization problem and constrained optimization problems can be formulated in a unified way. Secondly, we propose a geometric approach to solve optimal reinsurance problems directly. This paper considers a class of increasing convex ceded loss functions and derives the explicit solutions of the optimal reinsurance which can be in forms of quota-share, stop-loss, changeloss, the combination of quota-share and change-loss or the combination of change-loss and change-loss with different retentions. Finally, we consider two specific cases: Value at Risk (VaR) and Tail Value at Risk (TVaR).

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Optimal Reciprocal Reinsurance under GlueVaR Distortion Risk Measures

Huang¹,

Yin²

2019

JMF

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This article investigates the optimal reciprocal reinsurance strategies when the risk is measured by a general risk measure, namely the GlueVaR distortion risk measures, which can be expressed as a linear combination of two tail value at risk (TVaR) and one value at risk (VaR) risk measures. When we consider the reciprocal reinsurance, the linear combination of three risk measures can be difficult to deal with. In order to overcome difficulties, we give a new form of the GlueVaR distortion risk measures. This paper not only derives the necessary and sufficient condition that guarantees the optimality of marginal indemnification functions (MIF), but also obtains explicit solutions of the optimal reinsurance design. This method is easy to understand and can be simplified calculation. To further illustrate the applicability of our results, we give a numerical example.

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Two Sufficient Conditions for Convex Ordering on Risk Aggregation

Abstract: We define new stochastic orders in higher dimensions called weak correlation orders. It is shown that weak correlation orders imply stop-loss order of sums of multivariate dependent risks with the same marginals. Moreover, some properties and relations of stochastic orders are discussed.

Cited by 3 publications

References 19 publications

Remarks on Equality of Two Distributions under Some Partial Orders

Remarks on Equality of Two Distributions under Some Partial Orders

A unifying approach to constrained and unconstrained optimal reinsurance

Optimal Reciprocal Reinsurance under GlueVaR Distortion Risk Measures

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