Capital Requirements and Optimal Investment with Solvency Probability Constraints

IMA Journal of Management Mathematics (2015), 26 (4), 345-375.

34 Pages Posted: 9 Apr 2012 Last revised: 3 Sep 2015

See all articles by Alexandru Vali Asimit

Alexandru Vali Asimit

Cass Business School, City, University of London

Alex Badescu

University of Calgary

Tak-Kuen Siu

Macquarie University, Macquarie Business School

Yuriy Zinchenko

University of Calgary - Department of Mathematics and Statistics

Date Written: January 22, 2014

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

Suggested Citation

Asimit, Alexandru Vali and Badescu, Alex and Siu, Tak-Kuen and Zinchenko, Yuriy, Capital Requirements and Optimal Investment with Solvency Probability Constraints (January 22, 2014). IMA Journal of Management Mathematics (2015), 26 (4), 345-375. . Available at SSRN: https://ssrn.com/abstract=2037136 or http://dx.doi.org/10.2139/ssrn.2037136

Alexandru Vali Asimit

Cass Business School, City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Alex Badescu (Contact Author)

University of Calgary ( email )

University of Calgary
Calgary, Alberta
Canada

Tak-Kuen Siu

Macquarie University, Macquarie Business School

New South Wales 2109
Australia

Yuriy Zinchenko

University of Calgary - Department of Mathematics and Statistics ( email )

Calgary, Alberta T2N 1N4
Canada

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