Portfolio Optimization under Solvency Constraints: A Dynamical Approach

Abstract

We develop portfolio optimization problems to a non-life insurance company for finding the minimum capital required, which simultaneously satisfy solvency and portfolio performance constraints. Motivated by standard insurance regulations, we consider solvency capital requirements based on three criteria: Ruin Probability, Conditional Value-at-Risk and Expected Policyholder Deficit ratio. We propose a novel semi-parametric formulation for each problem and explore the advantages of implementing this methodology over other potential approaches. When liabilities follow a Log-Normal distribution, we provide sufficient conditions for convexity for all our problems. Using different expected Return on Capital target levels, we construct efficient frontiers when portfolio assets are modelled with a special class of multivariate GARCH models. We found that the correlation between assets plays an important role in the behaviour of the optimal capital required and the portfolio structure. The stability and out-of-sample performance of our optimal solutions are empirically tested with respect to both, the solvency requirement and the portfolio performance, through a double rolling window estimation exercise. Our results indicate that a time-varying correlation model outperforms the constant and no-correlation counterparts.

Keywords: Portfolio optimization, Capital requirements, Solvency constraint, Multivariate GARCH, Double rolling window

JEL Classification: C58, G11, G22