Life insurance profit testing in the Solvency II framework

In this work the traditional profit test - "the process of assessing the profitability of an insurance contract in advance of it being written", as defined in the "Encyclopedia of Actuarial Science" - is built according to the principles of "market consistency"outlined in the Solvency II EU Directive, and applied to life insurance contracts. The case of profit sharing policies with a minimum interest rate guaranteed is proposed as a general "reference scheme" and analysed in detail (index-linked and unit-linked policies are easily recognised as being a particular case). The profit test is performed in a stochastic market framework, obtained with the joint (correlated) dynamics of the Cox, Ingersoll and Ross model for interest rates and the Black and Scholes model for equity prices, evaluating contracts by mean of Monte Carlo simulation. To ensure the governance of the production plan we propose several criteria inspired to the principles of "sound and prudent management"; moreover we address the question of performing the test in a "market consistent" way coherently with the engagement to the "own risk and solvency assessment", as defined by Article 45 of the Solvency II Directive. Finally, referring to a market case, we propose the structure of a report that outlines the results obtained in the profit test and that provides the adequate support to the governance process.