Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T16:04:05.419Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust hedging in incomplete markets

Published online by Cambridge University Press:  16 March 2018

SALLY SHEN ,
ANTOON PELSSER  and
PETER SCHOTMAN
SALLY SHEN
Affiliation:
Global Risk Institute, 55 University Avenue, Toronto, ON M5J 2H7, Canada and Network for Studies on Pensions, Aging and Retirement (e-mail: sshen@globalriskinstitute.org)
ANTOON PELSSER
Affiliation:
Network for Studies on Pensions, Aging and Retirement and Department of Finance, Maastricht University, PO BOX 616, 6200 MD Maastricht, The Netherlands
PETER SCHOTMAN
Affiliation:
Network for Studies on Pensions, Aging and Retirement and Department of Finance, Maastricht University, PO BOX 616, 6200 MD Maastricht, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

We considered a pension fund that needs to hedge uncertain long-term liabilities. We modeled the pension fund as a robust investor facing an incomplete market and fearing model uncertainty for the evolution of its liabilities. The robust agent is assumed to minimize the shortfall between the assets and liabilities under an endogenous worst-case scenario by means of solving a min–max robust optimization problem. When the funding ratio is low, robustness reduces the demand for risky assets. However, cherishing the hope of covering the liabilities, a substantial risk exposure is still optimal. A longer investment horizon or a higher funding ratio weakens the investor's fear of model misspecification. If the expected equity return is overestimated, the initial capital requirement for hedging can be decreased by following the robust strategy.

Keywords

G11G13Model uncertaintyrobust optimizationincomplete marketdynamic hedgingexpected shortfall
Type
Article
Information
Journal of Pension Economics & Finance , Volume 18 , Issue 3 , July 2019 , pp. 473 - 493
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, E., Hansen, L., and Sargent, T. (2003) A quartet of semigroups for model specification, robustness, prices of risk, and model detection. Journal of the European Economic Association, 1(1): 68–123.Google Scholar
Ang, A., Chen, B., and Sundaresan, S. (2013) Liability-driven investment with downside risk. Journal of Portfolio Management, 40(1): 71.Google Scholar
Benjamin, B. and Soliman, A. S. (1993) Mortality on the Move: Methods of Mortality Projection. Oxford: Actuarial Education Service.Google Scholar
Blake, D. and Burrows, W. (2001) Survivor bonds: helping to hedge mortality risk. Journal of Risk and Insurance, 68: 339–348.Google Scholar
Brennan, M. J. (1998) The role of learning in dynamic portfolio decisions. European Finance Review, 1(3): 295–306.Google Scholar
Cairns, A. J., Blake, D., and Dowd, K. (2006) A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73(4): 687–718.Google Scholar
Cochrane, J. H. and Saa-Requejo, J. (2000) Beyond arbitrage: good-deal asset price bounds in incomplete markets. Journal of Political Economy, 108(1): 79–119.Google Scholar
Coelho, E. and Nunes, L. C. (2011) Forecasting mortality in the event of a structural change. Journal of the Royal Statistical Society: Series A (Statistics in Society), 174(3): 713–736.Google Scholar
Cvitanić, J. and Karatzas, I. (1999) On dynamic measures of risk. Finance and Stochastics, 3(4): 451–482.Google Scholar
Delbaen, F. (2002) Coherent Risk Measures on General Probability Spaces. Advances in Finance and Stochastics. Berlin, Heidelberg: Springer, pp. 1–37.Google Scholar
Detemple, J. and Rindisbacher, M. (2008) Dynamic asset liability management with tolerance for limited shortfalls. Insurance: Mathematics and Economics, 43(3): 281–294.Google Scholar
EIOPA, (2011) EIOPA Report on the fifth Quantitative Impact Study (QIS5) for Solvency II. EIOPA-TFQIS5-11/001, 14 March 2011. European Insurance and Occupational Pensions Authority.Google Scholar
Garlappi, L., Uppal, R., and Wang, T. (2006) Portfolio selection with parameter and model uncertainty: a multi-prior approach. The Review of Financial Studies, 20(1): 41–81.Google Scholar
Gilboa, I. and Schmeidler, D. (1989) Max–min expected utility with non-unique prior. Journal of Mathematical Economics, 18(2): 141–153.Google Scholar
Hansen, L. and Sargent, T. (2007) Robustness. Princeton, NJ: Princeton University Press.Google Scholar
Lee, R. and Carter, L. (1992) Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419): 659–671.Google Scholar
Li, J. S.-H., Hardy, M. R., and Tan, K. S. (2009) Uncertainty in mortality forecasting: an extension to the classical Lee-Carter approach. Astin Bulletin, 39(1): 137–164.Google Scholar
Luo, Y. (2016) Robustly strategic consumption–portfolio rules with informational frictions. Management Science, 63(12): 4158–4174.Google Scholar
Maenhout, P. (2004) Robust portfolio rules and asset pricing. Review of Financial Studies, 17(4): 951.Google Scholar
Margrabe, W. (1978) The value of an option to exchange one asset for another. The Journal of Finance, 33(1): 177–186.Google Scholar
McDonald, R., Cassano, M., and Fahlenbrach, R. (2006) Derivatives Markets, Volume 2. Boston: Addison-Wesley.Google Scholar
Merton, R. C. (1980) On estimating the expected return on the market: an exploratory investigation. Journal of Financial Economics, 8: 323–361.Google Scholar
Rockafellar, R. T. (1976) Monotone operators and the proximal point algorithm. SIAM Journal on Control and Optimization, 14(5): 877–898.Google Scholar
Sharpe, W. F. and Tint, L. G. (1990) Liabilities – a new approach. The Journal of Portfolio Management, 16(2): 5–10.Google Scholar
Turner, A. (2006) Pensions, risks, and capital markets. Journal of Risk and Insurance, 73(4): 559–574.Google Scholar
Van Berkum, F., Antonio, K., and Vellekoop, M. (2016) The impact of multiple structural changes on mortality predictions. Scandinavian Actuarial Journal, 2016(7):0 581–603.Google Scholar
Wang, N. (2009) Optimal consumption and asset allocation with unknown income growth. Journal of Monetary Economics, 56(4): 524–534.Google Scholar