Investing Towards an Exogenous Reference Level Using a Lower Partial Moments Criterion
This paper analyses an optimal investment problem, in which the agent aims to minimise a lower partial moments (LPM) criterion that depends on an exogenous
reference level. The problem concerns terminal wealth alone and is specified in an affine-term structure model. We derive closed-form expressions for the optimal portfolio rules and the optimal wealth process. Moreover, we analytically disentangle the distributional features of optimal terminal wealth. In the numerical illustrations,
we examine the problem in the context of a defined contribution (DC) pension scheme. The findings suggest that LPM-based investment policies can improve a pension
fund’s recovery potential. Despite their potentially outstanding performance, we illustrate that these policies may be difficult to implement. Furthermore, we show that the optima strongly depend on the estimates for the market prices of risk.