We describe the time dynamics of the solvency level of life insurance contracts by representing the solvency level and the underlying risk sources as the solution of a forward–backward system. This leads to an additive decomposition of the total solvency level with respect to time and different risk sources. The decomposition turns out to be an intuitive tool to study risk sensitivities. We study the forward–backward system and discuss two methods to obtain explicit representations: via linear partial differential equations and via a Monte Carlo method based on Malliavin calculus.
- backward stochastic differential equation
- life insurance risk management
- Malliavin calculus
- solvency level