A synthetic model for ALM in life insurance and numerical methods for SCR computation
We introduce a synthetic ALM model that catches the main specificity of life insurance contracts. First, it keeps track of both market and book values to apply the regulatory profit sharing rule. Second, it introduces a determination of the crediting rate to policyholders that is close to the practice and is a trade-off between the regulatory rate, a competitor rate and the available profits. Third, it considers an investment in bonds that enables to match a part of the cash outflow due to surrenders, while avoiding to store the trading history. We use this model to evaluate the Solvency Capital Requirement (SCR) with the standard formula, and illustrate the importance of matching cash-flows.
Then, we focus on the problem of evaluating the SCR at future dates. For this purpose, we study the multilevel Monte-Carlo estimator for the expectation of a maximum of conditional expectations. We obtain theoretical convergence results that complements the recent work of Giles and Goda. We then apply the MLMC estimator to the calculation of the SCR at future dates and compare it with estimators obtained with Least Squares Monte-Carlo or Neural Networks. Last, we discuss the effect of the portfolio allocation on the SCR at future dates.