×

zbMATH — the first resource for mathematics

A robust asset-liability management framework for investment products with guarantees. (English) Zbl 1352.90050
Summary: This paper suggests a robust asset-liability management framework for investment products with guarantees, such as guaranteed investment contracts and equity-linked notes. Stochastic programming and robust optimization approaches are introduced to deal with data uncertainty in asset returns and interest rates. The statistical properties of the probability distributions of uncertain parameters are incorporated in the model through appropriately selected symmetric and asymmetric uncertainty sets. Practical data-driven approaches for implementation of the robust models are also discussed. Numerical results using generated and real market data are presented to illustrate the performance of the robust asset-liability management strategies. The robust investment strategies show better performance in unfavorable market regimes than traditional stochastic programming approaches. The effectiveness of robust investment strategies can be improved by calibrating carefully the shape and the size of the uncertainty sets for asset returns.

MSC:
90B50 Management decision making, including multiple objectives
90B25 Reliability, availability, maintenance, inspection in operations research
90C15 Stochastic programming
91G10 Portfolio theory
Software:
YALMIP
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bacinello, AR, Fair valuation of a guaranteed life insurance participating contract embedding a surrender option, J Risk Insur, 70, 461-487, (2003)
[2] Ben-Tal, A; Nemirovski, A, Robust convex optimization, Math Oper Res, 23, 769-805, (1998) · Zbl 0977.90052
[3] Ben-Tal, A; Margalit, T; Nemirovski, A; Frenk, H (ed.); Roos, K (ed.); Terlaky, T (ed.); Zhang, S (ed.), Robust modeling of multi-stage portfolio problems, 303-328, (2000), Dordrecht · Zbl 1016.91055
[4] Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press, Princeton · Zbl 1221.90001
[5] Bertsimas, D; Pachamanova, D, Robust multiperiod portfolio management in the presence of transaction costs, Comput Oper Res, 35, 3-17, (2008) · Zbl 1139.91333
[6] Bertsimas, D; Pachamanova, D; Sim, M, Robust linear optimization under general norms, Oper Res Lett, 32, 510-516, (2004) · Zbl 1054.90046
[7] Boender, G; Dert, C; Heemskerk, F; Hoek, H; Zenios, SA (ed.); Ziemba, WT (ed.), A scenario approach of ALM, (2005), Amsterdam
[8] Brennan, MJ; Schwartz, ES, The pricing of equity-linked life insurance policies with an asset value guarantee, J Financ Econ, 3, 195-213, (1976)
[9] Brennan, MJ; Schwartz, ES, Alternative investment strategies for the issuers of equity linked life insurance policies with an asset value guarantee, J Bus, 52, 63-93, (1979)
[10] Chen, X; Sim, M; Sun, P, A robust optimization perspective on stochastic programming, Oper Res, 55, 1058-1071, (2007) · Zbl 1167.90608
[11] Consigli, G; Dempster, MAH, Dynamic stochastic programming for asset-liability management, Ann Oper Res, 81, 131-162, (1998) · Zbl 0908.90008
[12] Consiglio, A; Cocco, F; Zenios, SA, The value of integrative risk management for insurance products with guarantees, J Risk Financ, 2, 6-16, (2001)
[13] Consiglio, A; Saunders, D; Zenios, SA, Asset and liability management for insurance products with minimum guarantees: the UK case, J Bank Financ, 30, 645-667, (2006)
[14] Consiglio, A; Cocco, F; Zenios, SA, Asset and liability modeling for participating policies with guarantees, Eur J Oper Res, 186, 380-404, (2008) · Zbl 1138.91491
[15] Dantzig, GB; Infanger, G, Multi-stage stochastic linear programs for portfolio optimization, Ann Oper Res, 45, 59-76, (1993) · Zbl 0785.90008
[16] Duffee G (2002) The long-run behavior of firms stock returns: evidence and interpretations. Working paper, Haas School of Business, University of California at Berkeley, Berkeley, CA · Zbl 0785.90008
[17] Ghaoui, L; Lebret, H, Robust solutions to least-squares problems with uncertain data, SIAM J Matrix Anal Appl, 18, 1035-1064, (1997) · Zbl 0891.65039
[18] Escudero, LF; Garín, A; Merino, M; Pérez, G, On multistage stochastic integer programming for incorporating logical constraints in asset and liability management under uncertainty, Comput Manag Sci, 6, 307-327, (2009) · Zbl 1170.90452
[19] Fabozzi F, Kolm P, Pachamanova D, Focardi S (2007) Robust portfolio optimization and management. Wiley, Hoboken
[20] Ferstl, R; Weissensteiner, A, Asset-liability management under time varying investment opportunities, J Bank Financ, 35, 182-192, (2011)
[21] Gerstner, T; Griebel, M; Holtz, M; Goschnick, R; Haep, M, A general asset-liability management model for the efficient simulation of portfolios of life insurance policies, Insur Math Econ, 42, 704-716, (2008) · Zbl 1152.91581
[22] Goldfarb, D; Iyengar, G, Robust portfolio selection problem, Math Oper Res, 28, 1-37, (2003) · Zbl 1082.90082
[23] Gondzio, J; Kouwenberg, R, High performance computing for asset-liability management, Oper Res, 49, 879-891, (2001) · Zbl 1163.90548
[24] Goyal, A; Welch, I, A comprehensive look at the empirical performance of equity premium prediction, Rev Financ Stud, 21, 1455-1508, (2008)
[25] Gulpinar, N; Pachamanova, D, A robust optimization approach to asset-liability management under time-varying investment opportunities, J Bank Financ, 37, 2031-2041, (2013)
[26] Gulpinar, N; Rustem, B, Worst-case optimal robust decisions for multi-period portfolio optimization, Eur J Oper Res, 183, 981-1000, (2007) · Zbl 1138.91446
[27] Gulpinar, N; Rustem, B; Settergren, R, Simulation and optimization approaches to scenario generation, J Econ Dyn Control, 28, 1291-1315, (2004) · Zbl 1200.91280
[28] Hardy M (2003) Investment guarantees: modeling and risk management for equity-linked life insurance. Wiley, New York · Zbl 1092.91042
[29] Klaassen, P, Financial asset-pricing theory and stochastic programming models for asset-liability management, Manag Sci, 44, 31-48, (1998) · Zbl 1008.91503
[30] Kouwenberg, R, Scenario generation and stochastic programming models for asset liability management, Eur J Oper Res, 134, 279-292, (2001) · Zbl 1008.91050
[31] Löfberg J (2004) YALMIP: a toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD conference, Taipei, Taiwan
[32] Mallier, R; Alobaidi, G, Pricing equity-linked debt using the vasicek model, Acta Math Univ Comen, 71, 211-220, (2002) · Zbl 1073.91036
[33] Miltersen, KR; Persson, SA, Guaranteed investment contracts: distributed and undistributed excess return, Scand Actuar J, 4, 257-279, (2003) · Zbl 1092.91053
[34] Natarajan, K; Pachamanova, D; Sim, M, Incorporating asymmetric distributional information in robust value-at-risk optimization, Manag Sci, 54, 573-585, (2008) · Zbl 1142.91593
[35] Natarajan, K; Pachamanova, D; Sim, M, Constructing risk measures from uncertainty sets, Oper Res, 57, 1129-1141, (2009) · Zbl 1233.91153
[36] Nietert, B, Portfolio insurance and model uncertainty, OR Spectr, 25, 295-316, (2003) · Zbl 1043.91031
[37] Oguzsoy CB, Guven S (2007) Robust portfolio planning in the presence of market anomalies. OMEGA: Int J Manag Sci 35(1):1-6 · Zbl 1043.91031
[38] Pachamanova DA, Fabozzi FJ (2016) Portfolio construction and analytics. Wiley, Hoboken
[39] Pae, Y; Sabbaghi, N, Log-robust portfolio management after transaction costs, OR Spectr, 36, 95-112, (2014) · Zbl 1290.91150
[40] Pinar, M, Robust scenario optimization based on downside-risk measure for multi-period portfolio selection, OR Spectr, 29, 295-309, (2007) · Zbl 1126.91032
[41] Powell WB (2011) Approximate dynamic programming. Wiley, New York · Zbl 1242.90002
[42] Ramaswami M, Lieberman PK, Baez G (2001) Equity-linked notes. Global Equity Derivatives, Lehman Brothers
[43] Soyster AL, Murphy FH (2013) A unifying framework for duality and modeling in robust linear programs. OMEGA: Int J Manag Sci 41(6):984-997
[44] Stiefel, JD, The guaranteed investment contract (GIC), Soc Actuar, 36, 265-285, (1984)
[45] Toy, WW; Ryan, MD; Francis, JC (ed.); Toy, WW (ed.); Whittaker, JG (ed.), Public equity-linked debt, 329-342, (2000), New York
[46] Valle CA, Meade N, Beasley JE (2014) Absolute return portfolios. OMEGA: Int J Manag Sci 45:20-41 · Zbl 1290.91150
[47] Walsh MW (2008) Where did AIG’s cash go? The New York Times, October 30
[48] Ziemba WT, Mulvey JM (1998) Worldwide asset and liability modeling. Cambridge University Press, Cambridge
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.