Application of Frailty-Based Mortality Models Using Generalized Linear Models

Butt, Zoltan; Haberman, Steven

doi:10.2143/ast.34.1.504961

Cited by 17 publications

(27 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…All of the results that are commented on in this section are well known. We then skip the details, which can be found in the references already provided; see, for example, [2,19] or [3].…”

Section: Lifetime and Frailty: The Gompertz-gamma Modelmentioning

confidence: 99%

Frailty and Risk Classification for Life Annuity Portfolios

Olivieri

Pitacco

2016

Risks

View full text Add to dashboard Cite

Life annuities are attractive mainly for healthy people. In order to expand their business, in recent years, some insurers have started offering higher annuity rates to those whose health conditions are critical. Life annuity portfolios are then supposed to become larger and more heterogeneous. With respect to the insurer's risk profile, there is a trade-off between portfolio size and heterogeneity that we intend to investigate. In performing this, there is a second and possibly more important issue that we address. In actuarial practice, the different mortality levels of the several risk classes are obtained by applying adjustment coefficients to population mortality rates. Such a choice is not supported by a rigorous model. On the other hand, the heterogeneity of a population with respect to mortality can formally be described with a frailty model. We suggest adopting a frailty model for risk classification. We identify risk groups (or classes) within the population by assigning specific ranges of values to the frailty within each group. The different levels of mortality of the various groups are based on the conditional probability distributions of the frailty. Annuity rates for each class then can be easily justified, and a comprehensive investigation of insurer's liabilities can be performed.

show abstract

“…All of the results that are commented on in this section are well known. We then skip the details, which can be found in the references already provided; see, for example, [2,19] or [3].…”

Section: Lifetime and Frailty: The Gompertz-gamma Modelmentioning

confidence: 99%

Frailty and Risk Classification for Life Annuity Portfolios

Olivieri

Pitacco

2016

Risks

View full text Add to dashboard Cite

show abstract

“…The distribution F D of D specifies the portion of individuals whose mortality is lower or higher than a certain percentage of table mortality. It is characterized as follows (see, e.g., Ainslie, 2000, p. 44; Butt and Haberman, 2002, p. 5; Hougaard, 1984, pp. 75, 79; Pitacco, 2004, p. 15).…”

Section: Contract Valuationmentioning

confidence: 99%

“…According to the literature, the gamma distribution is a common choice for frailty models. It can thus also be employed for the stochastic differential mortality factor used in this article (see, e.g., Butt and Haberman, 2002, pp. 8–9; Hougaard, 1984, p. 76; Jones, 1998, p. 82; Olivieri, 2006, pp.…”

Section: Contract Valuationmentioning

confidence: 99%

Understanding the Death Benefit Switch Option in Universal Life Policies

Gatzert¹,

Schmitt-Hoermann²

2010

J of Risk & Insurance

View full text Add to dashboard Cite

UNIVERSAL LIFE POLICIES ABSTRACTUniversal life policies are the most popular insurance contract design in the United States. They have either a level death benefit paying a fixed face amount, or an increasing death benefit, which additionally to a fixed benefit pays the available cash value, and both types include the option to switch from one to the other. In this paper, we are interested in the fact that--unlike a switch from level to increasing--a switch from increasing to level death benefit requires neither fees nor additional evidence of insurability. To assess the impact of the death benefit switch option, we develop a model framework of increasing universal life policies embedding the option. Consideration of heterogeneity in respect of mortality via a stochastic frailty factor allows an investigation of adverse exercise behavior. In a comprehensive simulation analysis, we quantify the net present value of the option from the insurer's perspective using risk-neutral valuation under stochastic interest rates assuming empirical exercise probabilities. Based on our results, we provide policy recommendations for life insurers.

show abstract

“…Models 7and (8) are very common in practice, both for substandard and preferred risks, due to their simplicity; they are called age rating or age shifting models. Model (8), in particular, can be formally justified, assuming the Gompertz law for the standard force of mortality and the multiplicative model for differential mortality (see Benjamin and Pollard, 1993). In actuarial practice, the age-shifting is often applied directly to premium rates.…”

Section: Models For Differential Mortalitymentioning

confidence: 99%

“…In (9) mortality is adjusted in relation to age. Such a choice is common when annuities are dealt with.…”

Section: Models For Differential Mortalitymentioning

confidence: 99%