# Reparameterized Neural Network Approach

A defined-contribution pension member invests in cash, two nominal bonds, an inflation-linked bond and a stock index in a two-factor market, and may also buy term life insurance before retirement, with trading restricted to a non-empty closed convex constraint set. The approach builds a family of unconstrained artificial markets, computes dual upper bounds with a reparameterized neural network, and recovers feasible lower bounds via nested Monte Carlo and a Hamiltonian quadratic program. Relative duality gaps under two risk-aversion settings are below the SAMS and deep pricing kernel benchmarks, one of them at 2.87%.

A defined-contribution pension member invests in cash, two nominal bonds, an inflation-linked bond and a stock index in a two-factor market, and may also buy term life insurance before retirement, with trading restricted to a non-empty closed convex constraint set. The approach builds a family of unconstrained artificial markets, computes dual upper bounds with a reparameterized neural network, and recovers feasible lower bounds via nested Monte Carlo and a Hamiltonian quadratic program. Relative duality gaps under two risk-aversion settings are below the SAMS and deep pricing kernel benchmarks, one of them at 2.87%.