Abstract
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.
Highlights
On 10 October 2014, the European Commission adopted a Delegated Act regarding implementing rules for Solvency II
According to Quota-Share, we analytically describe how alternative methodologies3 to identify ceding commissions have an effect on the moments of the probability distribution of combined ratios and on the capital requirements for in the management practice, the insurer must usually choose among different efficient reinsurance strategies, taking into account either profitability sacrifice or capital saving
We present an Internal Model for Premium Risk for a multi-line Non-Life insurer to take into account the characteristics of each line of business (LoB) and the diversification effect due to the aggregation of them
Summary
On 10 October 2014, the European Commission adopted a Delegated Act (see [1]) regarding implementing rules for Solvency II. For Premium Risk, values of σprem,lob can be multiplied by a non-proportional factor NPlob in order to take into account existing Excess of Loss treaties This factor is set out at 80% for Property, Motor Third Party Liabilities (MTPL) and General Third Party Liabilities (GTPL) and at 100% for other LoBs. This factor is set out at 80% for Property, Motor Third Party Liabilities (MTPL) and General Third Party Liabilities (GTPL) and at 100% for other LoBs It is, allowed to use an undertaking specific approach (see Annex XVII of [1]) to derive an alternative estimate of NPlob based on the valuation of the reducing effect of XL treaty on the variability coefficient of the aggregate claim amount. MTPL, GTPL and Credit and Suretyship should have data over 15 years and other LoBs at least over 10 years
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