×

Portfolio optimization under Solvency II: a multi-objective approach incorporating market views and real-world constraints. (English) Zbl 1470.91239

Summary: We propose a new approach to handle the problem of portfolio optimization for non-life insurance company incorporating the solvency capital requirement (SCR), market views and their confident levels, several equality and inequality real-world constraints and transaction costs. We analyze two case studies: first, we consider a tri-objective optimization problem in which we minimize the market SCR, the variance of the so-called basic own funds (BOF) and maximize the return of portfolio; secondly, we consider bi-objective optimization problem in which we minimize the variance of BOF and maximize the return of portfolio while considering the market SCR as a constraint. We introduce a scenario-based framework in which the reference model is given by an internal model. By entropy pooling approach, we blended market views and their confident levels with the reference model to build the posterior distribution. The latter is used to compute the variance of BOF and the portfolio return. In both case studies, we obtain good results in term of risk-reward tradeoff and diversification.

MSC:

91G10 Portfolio theory
91G05 Actuarial mathematics

Software:

NMOF
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anagnostopoulos, KP; Mamanis, G., The mean-variance cardinality constrained portfolio optimization problem: an experimental evaluation of five multiobjective evolutionary algorithms, Expert Syst. Appl., 38, 11, 14208-14217 (2011)
[2] Black, F., Litterman R.: Asset allocation: combining investor views with market equilibrium. Goldman Sachs Fixed Income Res. (1990)
[3] Braun, A., Schmeiser, H., Schreiber, F.: Portfolio optimization under solvency II: implicit constraint imposed by the market risk standard formula. J Risk Insur (2015)
[4] Cont, R., Empirical properties of asset returns: stylized facts and statistical issues, Quant. Finance, 1, 223-36 (2001) · Zbl 1408.62174 · doi:10.1080/713665670
[5] Deb, K., An efficient constraint handling method for genetic algorithms, Comput. Methods Appl. Mech. Eng., 186, 2-4, 311-338 (2000) · Zbl 1028.90533 · doi:10.1016/S0045-7825(99)00389-8
[6] Deb, K., Multi-Objective Optimization using Evolutionary Algorithms (2001), New York: Wiley, New York · Zbl 0970.90091
[7] Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T., A fast and elitist multiobjective genetic algorithm, IEEE Trans. Evolut. Comput., 6, 2, 182-197 (2002) · doi:10.1109/4235.996017
[8] Di Tollo, G.; Roli, A., Metaheuristics for the portfolio selection problem, Int. J. Oper. Res., 5, 1, 13-35 (2008) · Zbl 1153.90587
[9] Embrechts, P., Actuarial versus financial pricing of insurance, J. Risk Finance, 1, 4, 17-26 (2000) · doi:10.1108/eb043451
[10] European Insurance and Occupational Pensions Authority (EIOPA), Technical Specifications for the Preparatory Phase (Part I). Available at: https://eiopa.europa.eu (2014)
[11] Fitch Ratings: Solvency II Set to Reshape Asset Allocation and Capital Markets. Insurance Rating Group Special Report (2011)
[12] Gilli, M.; Këllezi, E.; Hysi, H., A data-driven optimization heuristic for downside risk minimization, J. Risk, 8, 3, 1-16 (2006) · doi:10.21314/JOR.2006.129
[13] Gilli, M.; Maringer, D.; Schumann, E., Numerical Methods and Optimization in Finance (2011), New York: Academic Press, New York · Zbl 1236.91001
[14] Kaucic, M.; Daris, R., Multi-objective stochastic optimization programs for a non-life insurance company under solvency constraint, Risks, 2015, 3, 390-419 (2015) · doi:10.3390/risks3030390
[15] Kaucic, M.; Mojtaba, M.; Mohmmad, M., Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures, Financ. Innov., 5, 1, 5-34 (2019) · doi:10.1186/s40854-019-0140-6
[16] Konno, H.; Hiroshi, S.; Hiroaki, Y., A mean-absolute deviation-skewness portfolio optimization model, Ann. Oper. Res., 45, 205-220 (1993) · Zbl 0785.90014 · doi:10.1007/BF02282050
[17] Krink, T.; Paterlini, S., Multiobjective optimization using differential evolution for real-world portfolio optimization, Comput. Manag. Sci., 8, 157-179 (2011) · doi:10.1007/s10287-009-0107-6
[18] Markowitz, HM, Portfolio selection, J. Finance, 7, 1, 77-91 (1952)
[19] Meghwani, SS; Thakur, M., Multi-objective heuristic algorithms for practical portfolio optimization and rebalancing with transaction cost, Appl. Soft. Comput., 67, 865-894 (2018) · doi:10.1016/j.asoc.2017.09.025
[20] Metaxiotis, K.; Liagkouras, K., Multiobjective evolutionary algorithms for portfolio management: a comprehensive literature review, Expert Syst. Appl., 39, 14, 11685-11698 (2012) · doi:10.1016/j.eswa.2012.04.053
[21] Meucci, A., Beyond Black-Litterman in practice: a five-step recipe to input views on non-normal markets, Risk, 19, 114-119 (2006)
[22] Meucci, A., Fully flexible views: theory and practice, Risk, 21, 97-102 (2008)
[23] Meucci, A.: The Black-Litterman approach: original model and extensions. In: The Encyclopedia of Quantitative Finance, vol .1, pp. 196-199. Wiley, New York (2010)
[24] Mishra, SK; Panda, G.; Majhi, R., A comparative performance assessment of a set of multiobjective algorithms for constrained portfolio assets selection, Swarm Evol. Comput., 16, 38-51 (2014) · doi:10.1016/j.swevo.2014.01.001
[25] Pareto, V., Cours, D.: Economie Politique, Vols. I and II. F. Rouge, Lausanne (1986)
[26] Pezier, J.: Global portfolio optimization revisited: A least discrimination alternantive to Black-Litterman. ICMA Centre Discussion Papers in Finance (2007)
[27] Qian, E.; Gorman, S., Conditional distribution in portfolio theory, Financ. Anal. J., 57, 44-51 (2001) · doi:10.2469/faj.v57.n2.2432
[28] Roy, AD, Safety first and the holding of asset, Econometria, 20, 431-499 (1952) · Zbl 0047.38805 · doi:10.2307/1907413
[29] Sharpe, WF, Capital asset prices: a theory of market equilibrium under condition of risks, J. Finance, 19, 425-442 (1964)
[30] Tobin, J., Liquidity preference as behavior towards risk, Rev. Econ. Stud., 25, 1, 65-86 (1958) · doi:10.2307/2296205
[31] Zenios, SA, Practical Financial Optimization (2007), New York: Blackwell Publishing Ltd, New York · Zbl 1142.91008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.