Portfolio selection and consumption for individuals with truncated quadratic utilities and satiation points

Abstract

This paper studies the optimal life-cycle investment and consumption strategy of an agent with truncated quadratic preferences and a finite satiation point of utility, either for consumption or terminal wealth. Employing the dynamic programming and martingale methods, we derive explicit expressions for optimal policies in an unconstrained case where consumption and wealth are allowed to be negative, as well as a constrained case imposing a subsistence level for consumption and requiring that the terminal wealth must be non-negative. We allow for a general satiation point instead of taking the satiation/bliss level as the maximum point of the quadratic function. We reveal that when satiation does not occur, the lowering satiation point stimulates current consumption, while the increasing satiation point makes the risky asset more attractive. Furthermore, we demonstrate that the satiation levels of wealth and consumption are not always reached simultaneously. Interestingly, sensitivity analysis yields that wealth plays an important role in deciding the effect of mortality risk on consumption policy from a microcosmic perspective.