Life insurance mathematics

Abstract

The subject matter and methodology of modern life insurance mathematics are surveyed. Standard insurance products with payments depending only on life history events are described and analyzed in the commonly used Markov chain model under the assumption of deterministic interest rates. The actuarial equivalence principle for determining premiums and reserves is motivated by risk diversification in large portfolios. Differential equations for reserves and other conditional expected values are obtained and proclaimed basic constructive and computational tools. The traditional method for managing non-diversifiable risk arising from changes in e.g. mortality rates and interest rates is outlined; premiums are calculated under prudent assumptions, and systematic surpluses thus created are repaid as bonus. An alternative way of managing non-diversifiable risk is to link the contractual payments to the development of mortality, interest, and possibly other demographic or economic indexes. Examples of so-called index-linked products are given, and premiums and reserves are determined by combined use of classical actuarial principles and principles of pricing and hedging from financial mathematics. Transfer of non-diversifiable risk to the financial markets through creation of tradable insurance derivatives is outlined as an idea. Methods for estimation of mortality and other vital rates, formerly a major issue in life insurance mathematics, are fetched from modern statistical life history analysis and therefore only briefly described.