## A linear regression approach to modeling mortality rates of different forms.(English)Zbl 1414.91238

Summary: In this article, we propose a linear regression approach to modeling mortality rates of different forms. First, we repeat to fit a mortality sequence for each of $$K$$ years (called the fitting years) with another mortality sequence of equal length for some year (called the base year) differing by $$t_j$$ years $$(j=1,\dots,K)$$ using a simple linear regression. Then we fit the sequences of the estimated slope and intercept parameters of length $$K$$, respectively, with the sequence of $$\{t_j\}$$ by each of the simple linear regression and random walk with drift models. The sequences of the fitted slope and intercept parameters can be used for forecasting deterministic and stochastic mortality rates. Forecasting performances are compared among these two approaches and the Lee-Carter model. The CBD model is also included for comparisons for an elderly age group. Moreover, we give a central-death-rate-linked security to hedge mortality/longevity risks. Optimal units, purchased from the special purpose vehicle, which maximize the hedge effectiveness for life insurers and annuity providers, respectively, are derived and can be expressed in terms of the cumulative distribution function of the standard normal random variable. A measure with hedge cost involved, called hedge effectiveness rate, for comparing risk reduction amount per dollar spent among mortality models is proposed. Finally, numerical examples are presented for illustrations.

### MSC:

 91B30 Risk theory, insurance (MSC2010) 62P05 Applications of statistics to actuarial sciences and financial mathematics 62J05 Linear regression; mixed models

### Keywords:

stochastic mortality rates; linear regression
Full Text:

### References:

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