# Pension Fund

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%.

The study models two competing hybrid DC pension fund managers as a stochastic differential game in which liability risk follows a jump-diffusion process with truncated exponential jump amplitudes and the exact asset-to-liability ratio formulation is used, and it derives closed-form Nash equilibrium portfolio strategies and value functions via Hamilton–Jacobi–Bellman dynamic programming, finding that equilibrium weights are independent of liability jump parameters, reduce to K=(μ−r)/σ² and are independent of both managers' risk aversion in the symmetric liability-correlation case, that competition strictly amplifies risk-taking relative to the single-agent benchmark, and that a manager's own liability jumps reduce welfare while the competitor's jumps improve it.

The study models two competing hybrid DC pension fund managers as a stochastic differential game in which liability risk follows a jump-diffusion process with truncated exponential jump amplitudes and the exact asset-to-liability ratio formulation is used, and it derives closed-form Nash equilibrium portfolio strategies and value functions via Hamilton–Jacobi–Bellman dynamic programming, finding that equilibrium weights are independent of liability jump parameters, reduce to K=(μ−r)/σ² and are independent of both managers' risk aversion in the symmetric liability-correlation case, that competition strictly amplifies risk-taking relative to the single-agent benchmark, and that a manager's own liability jumps reduce welfare while the competitor's jumps improve it.