Note on option pricing by actuarial considerations

We study the asset allocation problem for a pension fund, which operates in a PAYG system and periodically revises its investment strategies. If the optimal amount of wealth invested in risky assets is always positive, then during the management period the optimal portfolio is constantly riskier (less risky) than Merton’s portfolio when the growth rate of workers is higher (lower) than the growth rate of pensioners. In particular, there exists a time when the risk exposure is a maximum (minimum).