IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v46y2010i2p317-327.html
   My bibliography  Save this article

A benchmarking approach to optimal asset allocation for insurers and pension funds

Author

Listed:
  • Lim, Andrew E.B.
  • Wong, Bernard

Abstract

We solve the optimal asset allocation problem for an insurer or pension fund by using a benchmarking approach. Under this approach the objective is an increasing function of the relative performance of the asset portfolio compared to a benchmark. The benchmark can be, for example, a function of an insurer's liability payments, or the (either contractual or target) payments of a pension fund. The benchmarking approach tolerates but progressively penalizes shortfalls, while at the same time progressively rewards outperformance. Working in a general, possibly non-Markovian setting, a solution to the optimization problem is presented, providing insights into the impact of benchmarking on the resulting optimal portfolio. We further illustrate the results with a detailed example involving an option based benchmark of particular interest to insurers and pension funds, and present closed form solutions.

Suggested Citation

  • Lim, Andrew E.B. & Wong, Bernard, 2010. "A benchmarking approach to optimal asset allocation for insurers and pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 317-327, April.
    • Handle: RePEc:eee:insuma:v:46:y:2010:i:2:p:317-327
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(09)00149-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Zengwu & Xia, Jianming & Zhang, Lihong, 2007. "Optimal investment for an insurer: The martingale approach," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 322-334, March.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Andrew E. B. Lim, 2004. "Quadratic Hedging and Mean-Variance Portfolio Selection with Random Parameters in an Incomplete Market," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 132-161, February.
    4. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    5. Mark Davis & SEBastien Lleo, 2008. "Risk-sensitive benchmarked asset management," Quantitative Finance, Taylor & Francis Journals, vol. 8(4), pages 415-426.
    6. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    7. Korn, Ralf & Wiese, Anke, 2008. "Optimal Investment and Bounded Ruin Probability: Constant Portfolio Strategies and Mean-variance Analysis 1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 423-440, November.
    8. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 843-877, May.
    9. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    10. Sid Browne, 2000. "Risk-Constrained Dynamic Active Portfolio Management," Management Science, INFORMS, vol. 46(9), pages 1188-1199, September.
    11. Xie, Shuxiang & Li, Zhongfei & Wang, Shouyang, 2008. "Continuous-time portfolio selection with liability: Mean-variance model and stochastic LQ approach," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 943-953, June.
    12. Gao, Jianwei, 2008. "Stochastic optimal control of DC pension funds," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1159-1164, June.
    13. Tepla, Lucie, 2001. "Optimal investment with minimum performance constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1629-1645, October.
    14. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    15. JULES H. Van BINSBERGEN & MICHAEL W. BRANDT & RALPH S. J. KOIJEN, 2008. "Optimal Decentralized Investment Management," Journal of Finance, American Finance Association, vol. 63(4), pages 1849-1895, August.
    16. Stanley R. Pliska, 1986. "A Stochastic Calculus Model of Continuous Trading: Optimal Portfolios," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 371-382, May.
    17. Xiao, Jianwu & Hong, Zhai & Qin, Chenglin, 2007. "The constant elasticity of variance (CEV) model and the Legendre transform-dual solution for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 302-310, March.
    18. Sid Browne, 1999. "Beating a moving target: Optimal portfolio strategies for outperforming a stochastic benchmark," Finance and Stochastics, Springer, vol. 3(3), pages 275-294.
    19. Chen, Ping & Yang, Hailiang & Yin, George, 2008. "Markowitz's mean-variance asset-liability management with regime switching: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 456-465, December.
    20. Cairns, Andrew, 2000. "Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 19-55, May.
    21. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    22. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    23. Wang, Nan, 2007. "Optimal investment for an insurer with exponential utility preference," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 77-84, January.
    24. Chiu, Mei Choi & Li, Duan, 2006. "Asset and liability management under a continuous-time mean-variance optimization framework," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 330-355, December.
    25. Eckhard Platen, 2005. "On The Role Of The Growth Optimal Portfolio In Finance," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 365-388, December.
    26. Detemple, Jérôme & Rindisbacher, Marcel, 2008. "Dynamic asset liability management with tolerance for limited shortfalls," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 281-294, December.
    27. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    28. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, June.
    29. Hans‐Peter Bermin, 2002. "A General Approach to Hedging Options: Applications to Barrier and Partial Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 199-218, July.
    30. Josa-Fombellida, Ricardo & Rincon-Zapatero, Juan Pablo, 2006. "Optimal investment decisions with a liability: The case of defined benefit pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 81-98, August.
    31. Blake, David & Cairns, Andrew J. G. & Dowd, Kevin, 2001. "Pensionmetrics: stochastic pension plan design and value-at-risk during the accumulation phase," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 187-215, October.
    32. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    33. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    34. Griselda Deelstra & Martino Grasselli & Pierre-François Koehl, 2000. "Optimal investment strategies in a CIR framework," ULB Institutional Repository 2013/7594, ULB -- Universite Libre de Bruxelles.
    35. Jérôme Detemple & René Garcia & Marcel Rindisbacher, 2005. "Representation formulas for Malliavin derivatives of diffusion processes," Finance and Stochastics, Springer, vol. 9(3), pages 349-367, July.
    36. Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
    37. Boyle, Phelim & Imai, Junichi & Tan, Ken Seng, 2008. "Computation of optimal portfolios using simulation-based dimension reduction," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 327-338, December.
    38. de Jong, Frank, 2008. "Pension fund investments and the valuation of liabilities under conditional indexation," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 1-13, February.
    39. Boulier, Jean-Francois & Huang, ShaoJuan & Taillard, Gregory, 2001. "Optimal management under stochastic interest rates: the case of a protected defined contribution pension fund," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 173-189, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    2. Yueyang Zheng & Jingtao Shi, 2020. "A Stackelberg Game of Backward Stochastic Differential Equations with Applications," Dynamic Games and Applications, Springer, vol. 10(4), pages 968-992, December.
    3. Chendi Ni & Yuying Li & Peter Forsyth & Ray Carroll, 2020. "Optimal Asset Allocation For Outperforming A Stochastic Benchmark Target," Papers 2006.15384, arXiv.org.
    4. Jan Baldeaux & Fung & Katja Ignatieva & Eckhard Platen, 2015. "A Hybrid Model for Pricing and Hedging of Long-dated Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(4), pages 366-398, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
    2. Han, Nan-wei & Hung, Mao-wei, 2012. "Optimal asset allocation for DC pension plans under inflation," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 172-181.
    3. Hong‐Chih Huang, 2010. "Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 451-472, June.
    4. Chang, Hao, 2015. "Dynamic mean–variance portfolio selection with liability and stochastic interest rate," Economic Modelling, Elsevier, vol. 51(C), pages 172-182.
    5. Zhao, Hui & Rong, Ximin & Zhao, Yonggan, 2013. "Optimal excess-of-loss reinsurance and investment problem for an insurer with jump–diffusion risk process under the Heston model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 504-514.
    6. Francesco, MENONCIN, 2003. "Optimal Real Consumption and Asset Allocation for a HARA Investor with Labour Income," LIDAM Discussion Papers IRES 2003015, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    7. Zhao, Hui & Rong, Ximin, 2012. "Portfolio selection problem with multiple risky assets under the constant elasticity of variance model," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 179-190.
    8. Di Giacinto, Marina & Federico, Salvatore & Gozzi, Fausto & Vigna, Elena, 2014. "Income drawdown option with minimum guarantee," European Journal of Operational Research, Elsevier, vol. 234(3), pages 610-624.
    9. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    10. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    11. Zheng, Xiaoxiao & Zhou, Jieming & Sun, Zhongyang, 2016. "Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 77-87.
    12. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    13. Yao, Haixiang & Yang, Zhou & Chen, Ping, 2013. "Markowitz’s mean–variance defined contribution pension fund management under inflation: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 851-863.
    14. Zhu, Huiming & Deng, Chao & Yue, Shengjie & Deng, Yingchun, 2015. "Optimal reinsurance and investment problem for an insurer with counterparty risk," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 242-254.
    15. Guan, Guohui & Liang, Zongxia, 2014. "Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 105-115.
    16. Guan, Guohui & Liang, Zongxia, 2015. "Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 99-109.
    17. Chang Hao & Wang Chunfeng & Fang Zhenming, 2017. "Portfolio Selection with Random Liability and Affine Interest Rate in the Mean-Variance Framework," Journal of Systems Science and Information, De Gruyter, vol. 5(3), pages 229-249, June.
    18. Francesco Menoncin & Elena Vigna, 2013. "Mean-variance target-based optimisation in DC plan with stochastic interest rate," Carlo Alberto Notebooks 337, Collegio Carlo Alberto.
    19. Tang, Mei-Ling & Chen, Son-Nan & Lai, Gene C. & Wu, Ting-Pin, 2018. "Asset allocation for a DC pension fund under stochastic interest rates and inflation-protected guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 87-104.
    20. Chang Guo & Xiaoyang Zhuo & Corina Constantinescu & Olivier Menoukeu Pamen, 2018. "Optimal Reinsurance-Investment Strategy Under Risks of Interest Rate, Exchange Rate and Inflation," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1477-1502, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:46:y:2010:i:2:p:317-327. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.