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Liability Driven Investments under a Benchmark Based Approach

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Abstract

In this paper, we present an alternative approach as a suitable framework under which liability driven investments can be valued and hedged. This benchmark approach values both assets and liabilities consistently under the real world probability measure using the best performing portfolio, the growth optimal portfolio, as benchmark and numeraire. The benchmark approach identifies the investment strategy which is replicating a given claim at minimal cost. Should the liability under consideration be subject to nonhedgeable risk, e.g. mortality risk, benchmarked risk minimization identifies with its real world pricing formula the investment strategy which minimizes in a practical sense the price of a given claim and minimizes the benchmarked profit and loss from hedging. The application of the approach will be demonstrated for pensions. A least expensive pension scheme will be described that allows one in a fair and transparent manner to hedge in the least expensive way with minimal risk the post retirement payments for its members.

Suggested Citation

  • Jan Baldeaux & Eckhard Platen, 2013. "Liability Driven Investments under a Benchmark Based Approach," Research Paper Series 325, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:325
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp325.pdf
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    References listed on IDEAS

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    1. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1, July-Dece.
    2. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Harry M. Markowitz, 2011. "Investment for the Long Run: New Evidence for an Old Rule," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 35, pages 495-508, World Scientific Publishing Co. Pte. Ltd..
    4. Henry Allen Latane, 1959. "Criteria for Choice Among Risky Ventures," Journal of Political Economy, University of Chicago Press, vol. 67(2), pages 144-144.
    5. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    7. Johnny Siu-Hang Li & Mary Hardy & Ken Seng Tan, 2008. "Threshold Life Tables and Their Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(2), pages 99-115.
    8. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    9. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 184, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Ke Du & Eckhard Platen, 2016. "Benchmarked Risk Minimization," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 617-637, July.
    12. Eckhard Platen & Hardy Hulley, 2008. "Hedging for the Long Run," Research Paper Series 214, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Ngoc Huy Chau & Wolfgang Runggaldier & Peter Tankov, 2016. "Arbitrage and utility maximization in market models with an insider," Papers 1608.02068, arXiv.org, revised Sep 2016.
    2. Cousin, Areski & Jiao, Ying & Robert, Christian Y. & Zerbib, Olivier David, 2016. "Asset allocation strategies in the presence of liability constraints," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 327-338.

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    More about this item

    Keywords

    liability driven investment; benchmark approach; least expensive pensions;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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