Optimal benefits, contributions, and asset allocation for a PAYG system with reserve fund under equity, longevity, and unemployment risks

We develop a discrete-time stochastic control model to jointly optimize benefits, contributions, and asset allocation in a PAYG pension system with a reserve fund under equity, longevity, and unemployment risks. We compare optimal policies and expected welfare for (i) a pure PAYG system, (ii) a PAYG system with an established reserve fund, and (iii) the transition phase between those two systems when a newly established fund is capitalized initially to a target level. We find that the reserve fund improves expected welfare for both the working and retired populations, delivering higher average benefits and lower average contribution rates despite added volatility from the equity exposure. Even when the fund is built up from zero during the transition phase, expected welfare improves, although the utility of some cohorts are adversely affected.