Robust Longevity Risk Management

40 Pages Posted: 27 Feb 2015

See all articles by Hong Li

Hong Li

Warren Centre for Actuarial Studies and Research, University of Manitoba

Anja De Waegenaere

Tilburg University - Department of Econometrics & OR, Netspar, and CentER

Bertrand Melenberg

Tilburg University - Center for Economic Research (CentER)

Date Written: December 31, 2014

Abstract

We consider longevity risk hedging problems, where survivor swaps are available as hedging instruments. As objective functions we consider the mean-variance and the mean-conditional-value-at-risk of the hedged liabilities, evaluated using an estimated probability law governing the mortality dynamics. To be robust against estimation inaccuracy, we optimize the worst-case value of the objective function, where the worst-case is with respect to a statistical confidence set around the estimated probability law. We derive reformulations of the worst-case optimization problems that can be solved easily. In the empirical analysis, we compare the performance of the worst case (robust) optimizations with the (non-robust) optimizations that ignore the estimation inaccuracy. We find that the robust optimizations perform better when the actual and estimated probability laws deviate, which is likely to happen in the presence of estimation inaccuracy.

Keywords: longevity risk, robust hedging, Kullback-Leibler divergence, mean-variance, conditional-value-at-risk

Suggested Citation

Li, Hong and De Waegenaere, Anja M.B. and Melenberg, Bertrand, Robust Longevity Risk Management (December 31, 2014). Netspar Discussion Paper No. 12/2014-073. Available at SSRN: https://ssrn.com/abstract=2569680 or http://dx.doi.org/10.2139/ssrn.2569680

Hong Li

Warren Centre for Actuarial Studies and Research, University of Manitoba ( email )

638 Drake Centre, 181 Freedman Crescent
Winnipeg, MB R3T 2N2
Canada

Anja M.B. De Waegenaere (Contact Author)

Tilburg University - Department of Econometrics & OR, Netspar, and CentER ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Bertrand Melenberg

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 2730 (Phone)

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