Measurement and control of technical risk in a life insurance company.

Summary With the development of the marketing of life insurance products, and in particular risk products, the market participants are led to question the technical bases constituting their activity. Thus, the control of technical risk has become a major challenge for a life insurance company. Even though risk management is at the heart of the insurer's activity, the latter must have the means to meet its commitments. This requirement requires, on the one hand, the analysis of past observations, on the other hand, the forecasting of future commitments, and finally the reaction to these analyses, aiming at establishing a conformity between knowledge and the strategy of its development. In response to these three problems, three parts successively detail the observation, forecasting and control of technical risk, studied as a non-financial cause of discrepancies between forecasts and actual activity. These parts are organized in order to gradually summarize the information available to a life insurance company, and the insurance business is analyzed here on the basis of its monetary components. The observation of the technical risk is thus approached through precise non-parametric estimation techniques, in order to describe both frequencies and amounts of payments. Some extensions of estimation principles and original estimators follow. Forecasting is then carried out through probabilistic modelling, moving from individual to collective models, followed by proposals for gain and risk indicators, favouring those derived from the theory of ruin. Several existing methods are then extended. These parts aim at progressively characterizing the monetary activity of an insurance company with the help of a stochastic process with jumps, from which is finally presented an original approach to cover the technical risk, illustrated by the reinsurance operation. The paper provides a particular insight into the selection of random prospects and the evaluation of risk prices.