Generalized Initial Premium in XL Reinsurance with Reinstatements

2010 ◽  
Author(s):  
Paola Ferretti ◽  
Antonella Campana
Keyword(s):  
Xl Reinsurance

scholarly journals Pricing catastrophe reinsurance under the standard deviation premium principle

2021 ◽  
Vol 7 (3) ◽  
pp. 4472-4484
Author(s):  
Wen Chao ◽  
Keyword(s):  
Standard Deviation ◽  
Extreme Value Theory ◽  
Value Theory ◽  
Catastrophic Loss ◽  
Peak Over Threshold ◽  
Earthquake Loss ◽  
Xl Reinsurance ◽  
Catastrophe Reinsurance ◽  
Core Problem ◽  
Pricing Formula

<abstract><p>Catastrophe reinsurance is an important way to prevent and resolve catastrophe risks. As a consequence, the pricing of catastrophe reinsurance becomes a core problem in catastrophic risk management field. Due to the severity of catastrophe loss, the Peak Over Threshold (POT) model in extreme value theory (EVT) is extensively applied to capture the tail characteristics of catastrophic loss distribution. However, there is little research available on the pricing formula of catastrophe excess of loss (Cat XL) reinsurance when the catastrophe loss is modeled by POT. In the context of POT model, we distinguish three different relations between retention and threshold, and then prove the explicit pricing formula respectively under the standard deviation premium principle. Furthermore, we fit POT model to the earthquake loss data in China during 1990–2016. Finally, we give the prices of earthquake reinsurance for different retention cases. The computational results illustrate that the pricing formulas obtained in this paper are valid and can provide basis for the pricing of Cat XL reinsurance contracts.</p></abstract>

scholarly journals Optimal Dynamic XL Reinsurance

2003 ◽  
Vol 33 (2) ◽  
pp. 193-207 ◽  
Author(s):  
Christian Hipp ◽  
Michael Vogt
Keyword(s):  
Ruin Probability ◽  
Bellman Equation ◽  
Compound Poisson Process ◽  
Risk Process ◽  
Infinite Time ◽  
Verification Theorem ◽  
Hamilton Jacobi Bellman Equation ◽  
Optimal Dynamic ◽  
Xl Reinsurance ◽  
Hamilton Jacobi Bellman

We consider a risk process modelled as a compound Poisson process. We find the optimal dynamic unlimited excess of loss reinsurance strategy to minimize infinite time ruin probability, and prove the existence of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation as well as a verification theorem. Numerical examples with exponential, shifted exponential, and Pareto claims are given.

scholarly journals Optimal Dynamic XL Reinsurance

2003 ◽  
Vol 33 (02) ◽  
pp. 193-207 ◽  
Author(s):  
Christian Hipp ◽  
Michael Vogt
Keyword(s):  
Ruin Probability ◽  
Bellman Equation ◽  
Compound Poisson Process ◽  
Risk Process ◽  
Infinite Time ◽  
Verification Theorem ◽  
Hamilton Jacobi Bellman Equation ◽  
Optimal Dynamic ◽  
Xl Reinsurance ◽  
Hamilton Jacobi Bellman

We consider a risk process modelled as a compound Poisson process. We find the optimal dynamic unlimited excess of loss reinsurance strategy to minimize infinite time ruin probability, and prove the existence of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation as well as a verification theorem. Numerical examples with exponential, shifted exponential, and Pareto claims are given.

scholarly journals On Pareto Conjugate Priors and Their Application to Large Claims Reinsurance Premium Calculation

2007 ◽  
Vol 37 (02) ◽  
pp. 405-428 ◽  
Author(s):  
José L. Vilar-Zanón ◽  
Cristina Lozano-Colomer
Keyword(s):  
Gamma Distribution ◽  
Shape Parameter ◽  
Generalized Inverse ◽  
Inverse Gaussian ◽  
Conjugate Priors ◽  
Pareto Distributions ◽  
Premium Calculation ◽  
History Of ◽  
Xl Reinsurance ◽  
Generalized Inverse Gaussian

This paper addresses the Bayesian estimation of the shape parameter of Pareto distributions, and its application to premium calculation of large claims excess of loss (XL) reinsurance contracts. It studies the use of the generalized inverse Gaussian (GIG) as a Pareto prior conjugate, a family that contains as a particular case the gamma distribution. An exact credibility formula is deduced allowing the calculation of individual reinsurance premiums. These are premiums suited to the excesses history of a sole portfolio. A family of predictive distributions for the excesses is derived. We apply our exact credibility model to a sample of excesses arisen in ten Spanish portfolios of liability motor insurance from year 1992 to year 2001.

scholarly journals On Pareto Conjugate Priors and Their Application to Large Claims Reinsurance Premium Calculation

2007 ◽  
Vol 37 (2) ◽  
pp. 405-428 ◽  
Author(s):  
José L. Vilar-Zanón ◽  
Cristina Lozano-Colomer
Keyword(s):  
Gamma Distribution ◽  
Shape Parameter ◽  
Generalized Inverse ◽  
Inverse Gaussian ◽  
Conjugate Priors ◽  
Pareto Distributions ◽  
Premium Calculation ◽  
History Of ◽  
Xl Reinsurance ◽  
Generalized Inverse Gaussian

This paper addresses the Bayesian estimation of the shape parameter of Pareto distributions, and its application to premium calculation of large claims excess of loss (XL) reinsurance contracts. It studies the use of the generalized inverse Gaussian (GIG) as a Pareto prior conjugate, a family that contains as a particular case the gamma distribution. An exact credibility formula is deduced allowing the calculation of individual reinsurance premiums. These are premiums suited to the excesses history of a sole portfolio. A family of predictive distributions for the excesses is derived. We apply our exact credibility model to a sample of excesses arisen in ten Spanish portfolios of liability motor insurance from year 1992 to year 2001.

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