Safe-side requirements in the framework of multistate models for the insurances of the person (Q2711709)

The so-called ``safe-side'' requirement concerns the first-order basis (used to calculate premiums) and is expressed in terms of some quantities involving a given second-order basis (which is judged realistic) as well as the first-order basis itself. In life insurance mathematics, pricing valuations are usually carried out taking into account only the first moment of the present value of benefits and premiums, whilst no explicit consideration is given to any risk aspect of the distribution of future liabilities. However, a safety loading is implicitly included in premiums as well as in reserves by assigning values to the financial and demographic variables worse than those realistically expected. The safety loading represents also the expected profit of the insurer. According to this practice, in convectional life insurance mathematics the safe-side requirement is usually expressed via the formula of Homans, thus with reference to the components of the annual expected profit. In the framework of multistate models, only one safe-side requirement has been proposed which is based on the reserves. NEWLINENEWLINENEWLINEThis paper deals with safe-side requirements for the insurances of the person in the framework of Markov multistate models. Some safe-side requirements, each one involving expected profits, are formulated and the relations among them and with the requirement proposed by \textit{J. M. Hoem} [in: Trans. 23rd Int. Congr. of Actuaries, Helsinki, Vol. R, 171-202 (1988)] as well are shown.