  This paper considers the pricing of equity-linked life insurance contracts
with death and survival benefits in a general model with multiple stochastic
risk factors: interest rate, equity, volatility, unsystematic and systematic
mortality. We price the equity-linked contracts by assuming that the insurer
hedges the risks to reduce the local variance of the net asset value process
and requires a compensation for the non-hedgeable part of the liability in the
form of an instantaneous standard deviation risk margin. The price can then be
expressed as the solution of a system of non-linear partial differential
equations. We reformulate the problem as a backward stochastic differential
equation with jumps and solve it numerically by the use of efficient neural
networks. Sensitivity analysis is performed with respect to initial parameters
and an analysis of the accuracy of the approximation of the true price with our
neural networks is provided.
