Capital Requirements and Optimal Investment with Solvency Probability Constraints

Abstract

Quantifying the economic capital and optimally allocating it into portfolios of financial instruments are two key topics in the asset/liability management (ALM) of an insurance company. In general these problems are studied in the literature by minimizing standard risk measures such as the value at risk (VaR) and the conditional value at risk (CVaR). Motivated by Solvency II regulations, we introduce a novel "risk-return'' optimization problem to solve for the optimal required capital and the portfolio structure when the ruin probability is used as an insurance solvency constraint. The proposed approach relies on a semi-parametric setting using scenario-based asset returns and different parametric assumptions for the liability distribution. Extensive simulations are provided to assess the sensitivity and robustness of our solutions relative to model factors.

Keywords: Optimal investment, Portfolio efficient frontier, Risk Capital, Ruin probability constraint, Second order cone programming, Solvency II, Value at Risk

JEL Classification: C61, E22, G11, G22