scholarly journals Chains of Reinsurance Revisited

1986 ◽  
Vol 16 (2) ◽  
pp. 77-88 ◽  
Author(s):  
Jean Lemaire ◽  
Jean-Pierre Quairiere
Keyword(s):  
Utility Functions ◽  
Exponential Utility ◽  
Pareto Optimal ◽  
Optimal Reinsurance ◽  
Special Case

AbstractChains of reinsurance were first modelled by Gerber, in a special case. It is shown that more general results can be obtained by applying Borch's theorem. The Pareto-optimal reinsurance indemnities are uniquely determined using the only assumption that the participating companies use exponential utility functions. A simple comparison then shows that Gerber's indemnities are not Pareto-optimal. Even if no assumption at all is introduced, the indemnities are shown to be closely linked to the risk aversions of the participants.

scholarly journals Estimation of Approximate Values of the Optimum Points on Efficient Portfolios Curve

2007 ◽  
Vol 6 (1) ◽  
pp. 99-106
Author(s):  
Henryk Kowgier
Keyword(s):  
Utility Functions ◽  
Exponential Utility ◽  
Efficient Portfolios

Estimation of Approximate Values of the Optimum Points on Efficient Portfolios Curve In the paper a method is found for estimating approximate optimum points on efficient portfolios curve (risk-profit) that are connected with exponential utility functions being very frequently preferred in practice by investors.

scholarly journals Optimal Reinsurance-Investment Problem under a CEV Model: Stochastic Differential Game Formulation

2020 ◽  
Vol 2020 ◽  
pp. 1-19 ◽  
Author(s):  
Danping Li ◽  
Ruiqing Chen ◽  
Cunfang Li
Keyword(s):  
Differential Game ◽  
Exponential Utility ◽  
Insurance Companies ◽  
Stochastic Differential Game ◽  
Investment Strategies ◽  
Small Company ◽  
Cev Model ◽  
Constant Elasticity ◽  
Optimal Reinsurance ◽  
Constant Elasticity Of Variance

This paper focuses on a stochastic differential game played between two insurance companies, a big one and a small one. In our model, the basic claim process is assumed to follow a Brownian motion with drift. Both of two insurance companies purchase the reinsurance, respectively. The big company has sufficient asset to invest in the risky asset which is described by the constant elasticity of variance (CEV) model and acquire new business like acting as a reinsurance company of other insurance companies, while the small company can invest in the risk-free asset and purchase reinsurance. The game studied here is zero-sum where there is a single exponential utility. The big company is trying to maximize the expected exponential utility of the terminal wealth to keep its advantage on surplus while simultaneously the small company is trying to minimize the same quantity to reduce its disadvantage. In this paper, we describe the Nash equilibrium of the game and prove a verification theorem for the exponential utility. By solving the corresponding Fleming-Bellman-Isaacs equations, we derive the optimal reinsurance and investment strategies. Furthermore, numerical examples are presented to show our results.

scholarly journals The Core of a Reinsurance Market

1981 ◽  
Vol 12 (1) ◽  
pp. 57-71 ◽  
Author(s):  
Bernard Baton ◽  
Jean Lemaire
Keyword(s):  
Pareto Optimality ◽  
Individual Rationality ◽  
Pareto Optimal ◽  
Collective Rationality ◽  
Important Special Case ◽  
The Core ◽  
Premium Calculation ◽  
The Individual ◽  
Special Case ◽  
Reinsurance Market

In a series of celebrated papers, K. Borch characterized the set of the Pareto-optimal risk exchange treaties in a reinsurance market. However, the Pareto-optimality and the individual rationality conditions, considered by Borch, do not preclude the possibility that a coalition of companies might be better off by seceding from the whole group. In this paper, we introduce this collective rationality condition and characterize the core of this game without transferable utilities in the important special case of exponential utilities. The mathematical conditions we obtain can be interpreted in terms of insurance premiums, calculated by means of the zero-utility premium calculation principle. We then show that the core is always non-void and conclude by an example.

Stochastic Pareto-optimal reinsurance policies

2013 ◽  
Vol 53 (3) ◽  
pp. 671-677 ◽  
Author(s):  
Xudong Zeng ◽  
Shangzhen Luo
Keyword(s):  
Pareto Optimal ◽  
Optimal Reinsurance

scholarly journals An Extension of the Gerber-Bühlmann-Jewell Conditions for Optimal Risk Sharing

2004 ◽  
Vol 34 (1) ◽  
pp. 27-48 ◽  
Author(s):  
Marek Kaluszka
Keyword(s):  
Risk Sharing ◽  
Sufficient Conditions ◽  
Utility Functions ◽  
Optimal Reinsurance ◽  
Optimal Insurance ◽  
Insurance Contracts ◽  
Optimal Dividend ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient ◽  
Optimal Risk Sharing

We provide necessary and sufficient conditions for optimality of mutual contracts for risk sharing under constraints on premiums or utility functions of participants of the agreement. These conditions are an extension of those of the Borch, Gerber and Bühlmann-Jewell ones. Some applications to optimal insurance contracts, optimal dividend sharing and optimal reinsurance are given.

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