Operations Stochstiques de Capitalisation

This paper presents a stochastic model of capitalization which takes into account the financial risk in the actuarial processes. We first introduce a stochastic differential equation which allows us to define the capitalization and actualization processes. We use these concepts to present a new principle of premium calculation for the capitalization on operations, based on the equality between backward reserve and conditional expectation of the forward reserve. A generalization of the classical Thiele equation in life insurance is also given. Numerical examples illustrate the model.