Nonparametric estimation of multivariate distribution function for truncated and censored lifetime data

Abstract

1 A number of models for generating statistical data in various fields of insurance, including life insurance, pensions, and general insurance have been considered. It is shown that the insurance statistics data, as a rule, are truncated and censored, and often multivariate. We propose a non-parametric estimation of the distribution function for multivariate truncated-censored data in the form of a quasi-empirical distribution and a simple iterative algorithm for its construction. To check the accuracy of the proposed evaluation of the distribution function for truncated-censored data, simulation studies have been conducted, which showed its high efficiency. The proposed estimates have been tested for many years by the IAAC Group of Companies in the actuarial valuation of corporate social liabilities according to IAS 19 Employee Benefits. Apart from insurance, some results of the work can be used, for example in medicine, biology, demography, mathematical theory of reliability, etc.

Nonparametric modeling cash flows of insurance company

“…The main source of insurance statistics in the Russian Federation is the Register of Insurance (Co-Insurance) Policies and the Register of Claims and Early Termination Insurance (Co-Insurance) Policies. The Registers' formats and entry procedures are set in the insurer's internal documents, however it is the regulator (the Bank of Russia) 1 that specifies the compulsory data to be entered and kept by an insurer for at least 5 years from the date of the full performance of obligations under the policy.…”

“…In other words, the value s is seen under the random condition s / ∈ T s k , where the set 5 Hereinafter, a simple t represents the value t − τ 1 k . This does not lead to ambiguity since the intended value is always clear from the context T s k = {s : s ≤ d k } is called the truncation set or the truncating set (see [1]) associated with its S k .…”

“…Let us consider the definition of the IBNR in form (1). It is equivalent to expression (16), where the expected loss (expected value of insurance payments) is used as addends M k (s), k = 1, .…”

“…The deductible prevents from capturing data on claims below a certain fixed amount of money (left censoring), and the limit prevents from capturing the exact amount of claim (right censoring). The further reading provides additional factors of the truncating and/or censoring of insurance statistics data (for example see [1], [7]). This paper applies the ideas presented in one of the authors' works [2], [3] and generalizes them for the case of insurance policies with deductibles, applying qED estimate of the multivariate distribution function for censored data [4].…”