Mathematical and Statistical Methods for Actuarial Sciences and Finance

(Nora) #1

Managing demographic risk in enhanced pensions


Susanna Levantesi and Massimiliano Menzietti

Abstract.This paper deals with demographic risk analysis in Enhanced Pensions, i.e., long-
term care (LTC) insurance cover for the retired. Both disability and longevity risks affect such
cover. Specifically, we concentrate on the risk of systematic deviations between projected and
realised mortality and disability, adopting a multiple scenario approach. To this purpose we
study the behaviour of the random risk reserve. Moreover, we analyse the effect of demographic
risk on risk-based capital requirements, explaining how they can be reduced through either
safety loading or capital allocation strategies. A profit analysis is also considered.

Key words:long term care covers, enhanced pension, demographic risks, risk reserve, sol-
vency requirements

1 Introduction


The “Enhanced Pension” (EP) is a long-term care (LTC) insurance cover for the
retired. It offers an immediate life annuity that is increased once the insured becomes
LTC disabled and requires a single premium. EP is affected by demographic risks
(longevity and disability risks) arising from the uncertainty in future mortality and
disability trends that cause the risk of systematic deviations from the expected values.
Some analyses of these arguments have been performed by Ferri and Olivieri [1]
and Olivieri and Pitacco [6]. To evaluate such a risk we carry out an analysis taking
into account a multiple scenario approach. To define a set of projected scenarios we
consider general population statistics of mortality and disability.
We firstly analyse the behaviour of the risk reserve, then we define the capital
requirements necessary to guarantee the solvency of the insurer. Finally we study the
portfolio profitability. Such an analysis cannot be carried out by analytical tools, but
requires a Monte Carlo simulation model.
The paper is organised as follows. In Section 2 we define the actuarial framework
for EPs. In Section 3 we develop nine demographic scenarios and describe through a
suitable model how they can change over time. In Section 4 we present a risk theory
model based on the portfolio risk reserve and the Risk Based Capital requirements
necessary to preserve the insurance company from failures with a fixed confidence

M. Corazza et al. (eds.), Mathematical and Statistical Methodsfor Actuarial Sciencesand Finance
© Springer-Verlag Italia 2010

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