Abstract
In the paper, we introduce a multi-objective scenario-based optimization approach for chance-constrained portfolio selection problems. More specifically, a modified version of the normal constraint method is implemented with a global solver in order to generate a dotted approximation of the Pareto frontier for bi- and tri-objective programming problems. Numerical experiments are carried out on a set of portfolios to be optimized for an EU-based non-life insurance company. Both performance indicators and risk measures are managed as objectives. Results show that this procedure is effective and readily applicable to achieve suitable risk-reward tradeoff analysis.
Highlights
One of the most important aims in the insurance industry is to manage risk and capital properly.The first attempt in connecting solvency requirements to risk measures relies on the investment of a minimum capital required into a single security, often considered as a risk-free asset
We propose to estimate the objectives by combining the semiparametric approach recently proposed by [4] with the GARCH-extreme value theory (EVT)-Copula model in order to reduce the number of simulated scenario and to capture the dependence tail structure of asset return distributions more satisfactorily than traditional multivariate GARCH models and Copula-based models
We model the marginal distribution of the standardized innovations by subdividing the sample into three parts and by employing the generalized Pareto (GP) distribution estimation for the corresponding upper and lower tails and the Gaussian kernel estimate for the center of the distribution
Summary
The first attempt in connecting solvency requirements to risk measures relies on the investment of a minimum capital required into a single security, often considered as a risk-free asset. This choice has been proven to be non-optimal, whereas the investment in multiple traded assets results in being the correct alternative (see, for instance, [1] for an example and [2] for a theoretical introduction). In this process, the choices of the solvency margin and of the optimal portfolio are treated separately. A dynamic improvement of this approach is provided in [5], where the portfolio optimization is analyzed under three different solvency regimes
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