Stochastic actuarial valuations in double-indexed pension annuity assessment

Solvency and financial health are two basic aims an insurance company should pursue within Solvency II regulatory framework. The guidelines continuously proposed by the involved Institutions in refined and clarifier versions stabilize the relevance of the capital amount to be allocated for achieving safe financial positions. Product choices, in particular, together with investment decisions, can be considered a good flywheel to harness, in a context in which several stochastic variables impact on the financial values. Our interest in this paper concerns the life annuity section in the particular case of participating life annuity contracts, i.e. contracts with interest rate guarantee with a contextual right of participation to the firm profit. The usual architecture of these contracts is established on the basis of the financial risk control, being the financial context in very long time periods the pre-eminent risk driver the insurer wants to focus. Nevertheless we have to notice that the long term risks connected to this kind of obligations are not completely drained with the financial risk control being very working the systematic demographic betterment in mortality. In this paper we want to explore the construction of life annuity with profit participation appropriately survival-indexed, obtaining a product double indexed on both the financial and demographic risk driver. Following the guidelines proposed by Denuit et al in 2011. in this paper we reintroduce the contractual structure suggested by these Authors, but characterized by further guarantees concerning profitability from the point of view of the insureds, thanks to a profit sharing system. Aim of the study is the performance analysis of a portfolio of participating survival-indexed annuities within a riskiness context set out by the adverse deviations of the demographic and financial bases, deepening the interactions between the risk due the random fluctuations of the dynamic of the capital returns and the risk due to the systematic random fluctuations of the lifetime evolutionary trend