Capital Requirements and Optimal Investment with Solvency Probability Constraints

Asimit, A.V., Badescu, A., Siu, T. K. & Zinchenko, Y. (2015). Capital Requirements and Optimal Investment with Solvency Probability Constraints. IMA Journal of Management Mathematics, 26(4), pp. 345-375. doi: 10.1093/imaman/dpt029

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Abstract

Quantifying economic capital and optimally allocating it into portfolios of financial instruments are two key topics in the asset–liability management of an insurance company. In general, these problems are studied in the literature by minimizing standard risk measures such as the value at risk and the conditional VaR. Motivated by Solvency II regulations, we introduce a novel optimization problem to solve for the optimal required capital and the portfolio structure simultaneously, when the ruin probability is used as an insurance solvency constraint. Besides the generic optimal required capital and portfolio problem formulation, we propose a two-model hierarchy of optimization models, where both models admit the so-called second-order conic reformulation, in turn making them particularly well suited for numerics. The first model, albeit naively asserting the normality of the returns on assets and liabilities, under minor further simplifications admits a closed-form solution—a set of formulas, which may be used as simple decision-making guidelines in the analysis of more complex scenarios. A potentially more realistic second model aims to represent the ‘heavy-tailed’ nature of an insurer's liabilities more accurately, while also allowing arbitrary distributions of asset returns via a semi-parametric approach. Extensive numerical simulations illustrate the sensitivity and robustness of the proposed approach relative to the model's parameters. In addition, we explore the potential of insurance risk diversification and discuss if combining several liabilities into a single insurance portfolio may always be beneficial for the insurer. Finally, we propose an extension of the model with an expected return on capital constraint added.

Item Type: Article
Additional Information: This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Management Mathematics following peer review. The version of record Asimit, A. V., Badescu, A., Siu, T. K. & Zinchenko, Y. (2015). Capital Requirements and Optimal Investment with Solvency Probability Constraints. IMA Journal of Management Mathematics, 26(4), pp. 345-375 is available online at: http://dx.doi.org/10.1093/imaman/dpt029
Uncontrolled Keywords: optimal investment, portfolio efficient frontier, risk capital, chance constrained programming, Solvency II, second-order cone programming
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
Divisions: Cass Business School > Faculty of Actuarial Science & Insurance
Related URLs:
URI: http://openaccess.city.ac.uk/id/eprint/13146

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