Optimal quota-share reinsurance based on the mutual benefit of insurer and reinsurer
type: Item
instance of: scholarly article
title: Optimal quota-share reinsurance based on the mutual benefit of insurer and reinsurer
zbMATH Open document ID: 1461.91264
author: Nan Zhang
author: Zhuo Jin
author: Linyi Qian
author: Rongming Wang
published in: Journal of Computational and Applied Mathematics
publication date: 2018-06-13T00:00:00Z
review text: An insurer wants to buy proportional reinsurance for an exponentially distributed claim \(X\). Both, insurer and reinsurer use the same exponential utility function. The range of reinsurance is limited because both parties want to increase their expected utilities. The joint goal is to minimise the sum of some risk measure. More specifically, one looks for \[ \min_{b \in [0,1]}\{J(b X -P_I(b)-u^I) + J((1-b) X -P_R(b)-u^R)\}\;, \] where \(P_R(b) = (1+\theta) (1-b)\mathbb{E}[X]\) is the reinsurance premium, \(P_I(b) = P_0 - P_R(b)\) is the premium part of the insurer, and \(u^I\) and \(u^R\) are the initial capitals of the insurer and reinsurer, respectively. As risk measure \(J\), the following cases are treated: (1) ruin probability \(J(Y) = \mathbb{P}[Y > 0]\), (2) variance \(J(Y) = \mathrm{Var}[Y]\), (3) value-at-risk \(J(Y) = \mathrm{VaR}_\gamma = \inf\{L: \mathbb{P}[Y \le -L] \ge \gamma\}\), (4) tail-value-at-risk \(J(Y)= \mathrm{TVaR}_\gamma = (1-\gamma)^{-1} \int_\gamma^1 \mathrm{VaR}_q\;d q\), (5) generalized Dutch type I risk measure. The optimal retention levels can then be calculated. Several cases of the parameters have to be distinguished because of the expected utility constraint.
reviewed by: Hanspeter Schmidli
Mathematics Subject Classification ID: 91G05
Mathematics Subject Classification ID: 91B16
zbMATH DE Number: 6887292
zbMATH Keywords: joint survival probability
zbMATH Keywords: VaR
zbMATH Keywords: TVaR
zbMATH Keywords: quota-share reinsurance
zbMATH Keywords: utility improvement constraints
MaRDI profile type: Publication
full work available at URL: j.cam.2018.04.030
OpenAlex ID: W2799540256
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DOI: 10.1016/J.CAM.2018.04.030
description: scientific article; zbMATH DE number 6887292