TY - JOUR
T1 - Green nested simulation via likelihood ratio
T2 - Applications to longevity risk management
AU - Feng, Ben Mingbin
AU - Li, Johnny Siu Hang
AU - Zhou, Kenneth Q.
N1 - Funding Information:
This research is supported by Discovery Grants from the Natural Sciences and Engineering Research Council of Canada ( RGPIN-2018-03755 for B. Feng and RGPIN-2021-02409 for J.S.-H. Li) and a Centers of Actuarial Excellence (CAE) research grant from the Society of Actuaries CAE-2017 . The authors are thankful for the anonymous reviewers' many insightful comments and suggestions.
Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/9
Y1 - 2022/9
N2 - In the context of longevity risk, the nested simulation problem arises in various applications such as evaluating the effectiveness of longevity hedges and estimating solvency capital requirements. The standard nested simulation method demands a lot of computational effort, thereby making risk analyses in these applications difficult, especially in a practical setting when computing power is constrained. In this paper, we propose a green nested simulation (GNS) procedure for longevity risk management. The GNS procedure requires only small computations, achieves high accuracies, and is easy to implement. Mathematically, the GNS estimator is unbiased, and, in different modes of convergence, can achieve an arbitrary accuracy as the simulation budget increases. We demonstrate the GNS procedure with three numerical case studies. The empirical results indicate that the GNS procedure leads to estimates that are orders of magnitudes more accurate compared to the standard nested simulation, and also outperforms the existing approximation methods for getting around the nested simulation problem, particularly when the payoff under consideration is non-linear.
AB - In the context of longevity risk, the nested simulation problem arises in various applications such as evaluating the effectiveness of longevity hedges and estimating solvency capital requirements. The standard nested simulation method demands a lot of computational effort, thereby making risk analyses in these applications difficult, especially in a practical setting when computing power is constrained. In this paper, we propose a green nested simulation (GNS) procedure for longevity risk management. The GNS procedure requires only small computations, achieves high accuracies, and is easy to implement. Mathematically, the GNS estimator is unbiased, and, in different modes of convergence, can achieve an arbitrary accuracy as the simulation budget increases. We demonstrate the GNS procedure with three numerical case studies. The empirical results indicate that the GNS procedure leads to estimates that are orders of magnitudes more accurate compared to the standard nested simulation, and also outperforms the existing approximation methods for getting around the nested simulation problem, particularly when the payoff under consideration is non-linear.
KW - Likelihood ratio method
KW - Mortality-linked securities
KW - Nested simulation
KW - The Lee-Carter model
KW - Value hedges
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U2 - 10.1016/j.insmatheco.2022.07.004
DO - 10.1016/j.insmatheco.2022.07.004
M3 - Article
AN - SCOPUS:85134810031
SN - 0167-6687
VL - 106
SP - 285
EP - 301
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
ER -