Abstract
In actuarial science relative to pensions and life annuities, it is a common assumption that the discount rate used to calculate the adequate reserve amount to cover future payments is equal to the expected long-term return rate of portfolios in which it is invested. This assumption is inadequate because it could lead fund managers to take excessive risks in order to obtain greater profitability and not be aware that each future cash flow should have a discount rate in accordance with its payment date. This article demonstrates the existence of a suitable technical interest rate to discount each future payment. However, these rates are not necessarily equal among themselves and the expected long-term return of the portfolio. In order to estimate these technical interest rates, it is proposed to apply a risk model to each of the expected payments, which incorporates the fluctuations of the portfolio in which the actuarial reserves are invested. Calculating appropriate discount rates to determine actuarial reserves contributes to strengthening the stability of pension systems and the financial system in general.
Highlights
The calculation of the actuarial reserve necessary to cover all the payments of a life annuity is a fundamental issue for insurance companies, as well as governments and public or private entities paying their own pensions
In actuarial science relating to life annuities, it is generally assumed that the technical interest rate at which reserves are calculated to cover payments is equal to the expected rate of return of the portfolios where the reserves are invested, as indicated by Holsboer (2000) and Arango et al (2013)
This document shows a procedure to calculate the technical interest rates that should be used to discount each possible payment in the actuarial reserve necessary for a life annuity
Summary
The calculation of the actuarial reserve necessary to cover all the payments of a life annuity is a fundamental issue for insurance companies, as well as governments and public or private entities paying their own pensions. In actuarial science relating to life annuities, it is generally assumed that the technical interest rate at which reserves are calculated to cover payments is equal to the expected rate of return of the portfolios where the reserves are invested, as indicated by Holsboer (2000) and Arango et al (2013). This assumption is transversal to defined-contribution and defined-benefit plans, which is why the problem of choosing the best investment strategy to manage pension funds becomes extremely important in the management of such portfolios (Charupat & Milevsky, 2002). (8) (9) (10) where: : Frecuency of capitalization of interest compost model with nominal interest rate. : Future Value. : Present Value
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