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This paper considers the pricing of equity-linked life insurance contractswith death and survival benefits in a general model with multiple stochasticrisk factors: interest rate, equity, volatility, unsystematic and systematicmortality. We price the equity-linked contracts by assuming that the insurerhedges the risks to reduce the local variance of the net asset value processand requires a compensation for the non-hedgeable part of the liability in theform of an instantaneous standard deviation risk margin. The price can then beexpressed as the solution of a system of non-linear partial differentialequations. We reformulate the problem as a backward stochastic differentialequation with jumps and solve it numerically by the use of efficient neuralnetworks. Sensitivity analysis is performed with respect to initial parametersand an analysis of the accuracy of the approximation of the true price with ourneural networks is provided.

Pricing equity-linked life insurance contracts with multiple risk factors by neural networks