Portfolio Optimization under Solvency Constraints: A Dynamical Approach

North American Actuarial Journal, 2014, Volume 18, Issue 3, p.394-416

36 Pages Posted: 2 Mar 2013 Last revised: 17 Nov 2014

See all articles by Sujith Asanga

Sujith Asanga

University of Calgary - Department of Mathematics and Statistics

Alexandru Vali Asimit

Cass Business School, City, University of London

Alex Badescu

University of Calgary

Steven Haberman

City University London - Faculty of Actuarial Science

Date Written: February 28, 2013

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

Suggested Citation

Asanga, Sujith and Asimit, Alexandru Vali and Badescu, Alex and Haberman, Steven, Portfolio Optimization under Solvency Constraints: A Dynamical Approach (February 28, 2013). North American Actuarial Journal, 2014, Volume 18, Issue 3, p.394-416. Available at SSRN: https://ssrn.com/abstract=2226369 or http://dx.doi.org/10.2139/ssrn.2226369

Sujith Asanga

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

University of Calgary
Calgary, Alberta
Canada

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

Steven Haberman

City University London - Faculty of Actuarial Science ( email )

London
United Kingdom

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