##
**A semiparametric method for assessing life expectancy evaluations.**
*(English)*
Zbl 1479.91334

Summary: In the life settlements industry, life expectancy (LE) providers are firms that conduct health underwriting toward predicting the future mortality of an insured. Multiple stakeholders are interested in evaluating the quality of their assessments. There has been some recent interest in better alternatives to the traditional metric for this quality, the A/E ratio: the ratio of actual to expected number of deaths. One such alternative is the implied difference in life expectancies (IDLE) metric proposed by D. Bauer et al. [N. Am. Actuar. J. 22, No. 2, 198–209 (2018; Zbl 1393.91098)]. Its design largely retains the simplicity of the A/E ratio while being informative, unlike the A/E ratio, throughout the life of a policy block. Even though the IDLE is a significant improvement over the A/E ratio, it turns out that the IDLE is sensitive to departures from a key assumption, which motivates our development of a more robust metric. Our proposed methodology for evaluating the quality of the LE assessments involves using a survival regression model for estimating the mortality distribution of the insureds, with the average deviation of the life assessments from those derived using this model serving as a metric. In particular, we show that utilizing a Cox proportional hazards model with covariates derived from the LE assessments results in a robust yet well-performing alternative to both the A/E ratio and the IDLE.

### MSC:

91G05 | Actuarial mathematics |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

### Citations:

Zbl 1393.91098
PDF
BibTeX
XML
Cite

\textit{H. B. Lim} and \textit{N. D. Shyamalkumar}, N. Am. Actuar. J. 25, No. 3, 360--394 (2021; Zbl 1479.91334)

Full Text:
DOI

### References:

[1] | Actuarial Standards Board (2013) |

[2] | Best, A. M. (2016) |

[3] | American Academy of Actuaries and Society of Actuaries (2011) |

[4] | American Academy of Actuaries and Society of Actuaries (2018) |

[5] | Andersen, P. K.; Borgan, Ø.; Gill, R. D.; Keiding, N., Statistical models based on counting processes (1992), Springer-Verlag |

[6] | Andersen, P. K.; Gill., R. D., Cox’s regression model for counting processes: A large sample study, The Annals of Statistics, 10, 4, 1100-120 (1982) · Zbl 0526.62026 |

[7] | Anderson, J.; Cain, K.; Gelber., R., Analysis of survival by tumor response, Journal of Clinical Oncology, 1, 11, 710-19 (1983) |

[8] | Bauer, D.; Fasano, M. V.; Russ, J.; Zhu., N., Evaluating life expectancy evaluations, North American Actuarial Journal, 22, 2, 198-209 (2018) · Zbl 1393.91098 |

[9] | Braun, A.; Affolter, S.; Schmeiser., H., Life settlement funds: Current valuation practices and areas for improvement, Risk Management and Insurance Review, 19, 2, 173-95 (2015) |

[10] | Braun, A.; Cohen, L. H.; Malloy, C. J.; Xu, J., 218-127 (2018) |

[11] | Braun, A.; Cohen, L. H.; Malloy, C. J.; Xu, J. (2018) |

[12] | Braun, A.; Gatzert, N.; Schmeiser., H., Performance and risks of open-end life settlement funds, Risk Management and Insurance Review, 79, 1, 193-229 (2012) |

[13] | Dafni, U., Landmark analysis at the 25-year landmark point, Circulation: Cardiovascular Quality and Outcomes, 4, 3, 363-71 (2011) |

[14] | Davó, N. B.; Resco, C. M.; Barroso, M. M., Portfolio diversification with life settlements: an empirical analysis applied to mutual funds, The Geneva Papers, 38, 22-42 (2013) |

[15] | Deloitte (2005) |

[16] | Doherty, N. A.; Singer., H. J., The benefits of a secondary market for life insurance policies, Real Property, Probate and Trust Journal, 38, 3, 449-78 (2003) |

[17] | Emergent Capital Inc, 10-KT form (2018) |

[18] | European Life Settlement Association (2013) |

[19] | Gibson, C. (2019) |

[20] | ITM TwentyFirst (2019) |

[21] | Januário, A. V.; Naik, N. Y., Testing for adverse selection in life settlements: The secondary market for life insurance policies (2016) |

[22] | Keiding, N.; Gill., R. D., Random truncation models and Markov processes, The Annals of Statistics, 18, 2, 582-602 (1990) · Zbl 0717.62073 |

[23] | Klein, J. P.; Moeschberger, M. L., Survival analysis: Techniques for censored and truncated data (1998), New York: Springer, New York |

[24] | Kleinbaum, D. G.; Mitchel, K., Survival analysis: A self-learning text (2012), New York: Springer, New York |

[25] | R Core Team, R: A language and environment for statistical computing (2019), Vienna: R Foundation for Statistical Computing, Vienna |

[26] | Rao, R. R., The law of large numbers for. -valued random variables. Theory of Probability and its Applications (1963) · Zbl 0122.13303 |

[27] | Rosen, O.; Tanner., M., Mixtures of proportional hazards regression models, Statistics in Medicine, 18, 1119-131 (1999) |

[28] | Rouse, J., Fasano Conference 2017—Flawed longevity assumptions (2017) |

[29] | Sheridan, M., The STOLI worm: A practitioner’s guide to managing life settlements and micro longevity risk (2019) |

[30] | Society of Actuaries (2009) |

[31] | The Florida Legislature (2019) |

[32] | Therneau, T. M.; Grambsch., P. M., Proportional hazards tests and diagnostics based on weighted residuals, Biometrika, 81, 3, 515-526 (1994) · Zbl 0810.62096 |

[33] | Therneau, T. M.; Grambsch, P. M., Modeling survival data: Extending the Cox model (2000), New York: Springer, New York · Zbl 0958.62094 |

[34] | van der Vaart, A. W., Asymptotic statistics (1998), Cambridge University Press · Zbl 0910.62001 |

[35] | Xu, J., Dating death: An empirical comparison of medical underwriters in the U.S. life settlements market, North American Actuarial Journal, 24, 1, 36-56 (2020) · Zbl 1437.91401 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.