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The Impact of Reinsurance Strategies on Capital Requirements for Premium Risk in Insurance

by Gian Paolo Clemente 1,*,†, Nino Savelli 1,† and Diego Zappa 2,†
1
Department of Mathematics, Finance and Econometrics, Università Cattolica del Sacro Cuore, 20123 Milano, Italy
2
Department of Statistical Sciences, Università Cattolica del Sacro Cuore, 20123 Milano, Italy
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Weidong Tian
Risks 2015, 3(2), 164-182; https://doi.org/10.3390/risks3020164
Received: 31 March 2015 / Accepted: 26 May 2015 / Published: 3 June 2015
(This article belongs to the Special Issue Systemic Risk and Reinsurance)
New risk-based solvency requirements for insurance companies across European markets have been introduced by Solvency II and will come in force from 1 January 2016. These requirements, derived by a Standard Formula or an Internal Model, will be by far more risk-sensitive than the required solvency margin provided by the current legislation. In this regard, a Partial Internal Model for Premium Risk is developed here for a multi-line Non-Life insurer. We follow a classical approach based on a Collective Risk Model properly extended in order to consider not only the volatility of aggregate claim amounts but also expense volatility. To measure the effect of risk mitigation, suitable reinsurance strategies are pursued. We analyze how naïve coverage as conventional Quota Share and Excess of Loss reinsurance may modify the exact moments of the distribution of technical results. Furthermore, we investigate how alternative choices of commission rates in proportional treaties may affect the variability of distribution. Numerical results are also figured out in the last part of the paper with evidence of different effects for small and large companies. The main reasons for these differences are pointed out. View Full-Text
Keywords: capital requirement for premium risk; collective risk model; reinsurance strategies; Solvency II capital requirement for premium risk; collective risk model; reinsurance strategies; Solvency II
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Clemente, G.P.; Savelli, N.; Zappa, D. The Impact of Reinsurance Strategies on Capital Requirements for Premium Risk in Insurance. Risks 2015, 3, 164-182.

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