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 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.