TAILIEUCHUNG - FAIR PRICING OF LIFE INSURANCE PARTICIPATING POLICIES WITH A MINIMUM INTEREST RATE GUARANTEED

Farmers have several general concerns about crop insurance voiced by national farm organizations representing a cross-section of American agriculture. The American Farm Bureau Federation (AFBF) and others would like USDA to address shallow losses, which occur when losses are significant for the farmer but not enough to trigger an indemnity. 31 Also, this group and others point out a need to address declines in actual production history (APH), which is used for determining the insurance guarantee. Some farmers are subject to a declining insurance guarantee because of recent repeated disasters. (The American Sugar Cane League has commented on the inadequacy of. | FAIR PRICING OF LIFE INSURANCE PARTICIPATING POLICIES WITH A MINIMUM INTEREST RATE GUARANTEED BY Anna Rita Bacinello Dipartimento di Matematica Applicata alle Scienze Economiche Statistiche ed Attuariali Bruno de Finetti Università degli Studi di Trieste Trieste Italy. Abstract In this paper we analyse in a contingent-claims framework one of the most common life insurance policies sold in Italy during the last two decades. The policy of the endowment type is initially priced as a standard one given a mortality table and a technical interest rate. Subsequently at the end of each policy year the insurance company grants a bonus which is credited to the mathematical reserve and depends on the performance of a special investment portfolio. More precisely this bonus is determined in such a way that the total interest rate credited to the insured equals a given percentage participation level of the annual return on the reference portfolio and anyway does not fall below the technical rate minimum interest rate guaranteed henceforth . Moreover if the contract is paid by periodical premiums it is usually stated that the annual premium is adjusted at the same rate of the bonus and thus the benefit is also adjusted in the same measure. In such policy the variables controlled by the insurance company control-variables henceforth are the technical rate the participation level and in some sense the riskiness of the reference portfolio measured by its volatility. However as it is intuitive not all sets of values for these variables give rise to a fair contract . to a contract priced consistently with the usual assumptions on financial markets and in particular with no-arbitrage. We derive then necessary and sufficient conditions under which each control-variable is determined by a fair pricing of the contract given the remaining two ones. Keywords Policies with profits Minimum guarantee Fair pricing Black and Scholes framework. ASTIN BULLETIN. Vol. 31. No 2. 2001 pp. 275-297 .

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