Optimal strategies for target benefit pension plans with longevity risk in ambiguous environments

This paper studies the optimal investment and benefit adjustment of a target benefit pension plan under an ambiguous environment. Assume the pension manager invests in a risk-free asset, two risky assets, and a longevity asset. An optimal control model is developed with the objective of maximizing the terminal wealth and minimizing the combination of benefit-risk in terms of deviating from the target. The corresponding Hamilton-Jacobi-Bellman (HJB) equation is solved by using the dynamic programming method, and the explicit solutions of the optimal investment and benefit adjustment strategy are obtained. The numerical analysis found that longevity risk and smooth ambiguity have a great impact on the optimal investment strategy. When the manager is more averse to ambiguity, the manager will invest less in the ambiguous asset.