Applied

Optimal investment is a key problem in asset-liability management of an insurance company. Rather than allocating wealth optimally so as to maximize the overall investment return, an insurance company is interested in assessing the risk exposure where both assets and liabilities are included and minimizing the risk of mismatches between them. Different approaches for solving optimization problems by minimizing standard risk measures such as the value at risk (VaR) or the conditional value at risk (CVaR) have been proposed in the literature. In this paper we focus on some Solvency II applications by investigating several novel problems for jointly quantifying the optimal initial capital requirement and the optimal portfolio investment under various constraints.

Discussions on the convexity of these problems are also provided. Using a Monte Carlo simulation and a semi-parametric approach based on different assumptions for the loss distribution, we compute the insurer optimal capital needed to be efficiently invested in a portfolio formed by two or more assets. Finally, a detailed numerical experiment is conducted to assess the robustness and sensitivity of our optimal solutions relative to the model factors.

This paper was written in collaboration with Alexandru V. Asimit (Cass Business School, City University, UK), Tak Kuen Siu (Faculty of Business and Economics, Macquarie University, Australia)and Yuriy Zinchenko (Department of Mathematics and Statistics, University of Calgary).