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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
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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 

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