Mean-Variance Portfolio Selection with Dynamic Targets for Expected Terminal Wealth

Abstract

In a market that consists of multiple stocks and one risk-free asset whose mean return rates and volatility are deterministic, we study a continuous-time mean-variance portfolio selection problem in which an agent is subject to a constraint that the expectation of her terminal wealth must exceed a target and minimizes the variance of her terminal wealth. The agent can revise her expected terminal wealth target dynamically to adapt to the change of her current wealth, and we consider the following three targets: (i) the agent's current wealth multiplied by a target expected gross return rate, (ii) the risk-free payoff of the agent's current wealth plus a premium, and (iii) a weighted average of the risk-free payoff of the agent's current wealth and a pre-set aspiration level. We derive the so-called equilibrium strategy in closed form for each of the three targets and find that the agent effectively minimizes the variance of the instantaneous change of her wealth subject to a certain constraint on the expectation of the instantaneous change of her wealth.

Keywords: portfolio selection, dynamic mean-variance analysis, time inconsistency, equilibrium policies

JEL Classification: G11, D81, C61