Numerical Solutions to Lump-Sum Pension Fund Problems that Can Yield Left-Skewed Fund Return Distributions

The paper is about pension fund problems where an agent pays an amount x0 to the fund manager and is repaid, after time T, a lump sum x(T). Such problems admit an analytical solution for specific, rather unrealistic formulations. Several practical pension fund problems are converted in the paper into Markov decision chains solvable through approximations. In particular, a couple of problems with a non-differentiable asymmetric (with respect to risk) utility function are solved, for which left-skewed fund-return distributions are reported. Such distributions ascribe more probability to higher payoffs than the right-skewed ones that are common among analytical solutions