Abstract: This paper is based on the self-control problem in real economy and the consistent performance requirement in investment practice. The existing literature has not researched on consumption and portfolio choices in a framework integrating time-inconsistent preferences and consistent performance. Considering time-varying impatience risk and consistent-performance constraint simultaneously, the paper studies their joint impacts on optimal consumption and portfolio allocation. According to Grenadier and Wang (2007), Harris and Laibson (2013), this paper characterizes time-inconsistent preference by a quasi-hyperbolic discount function in continuous time. According to Chen and Tian (2012), consistent-performance constraint is defined by that the current wealth must stays at least on the level given by a weighted average of wealth in the past.There are one risk-free asset and one risky asset in the financial market. Using dynamic programming approach and numerical methods, this paper gives the optimal weight of the risky asset and the optimal consumption. The results show that the tolerance to the withdrawal in wealth and the optimal proportional allocation in risky asset are determined by the degree of consistent performance constraint and the change of time preference. Firstly, given the degree of consistent-performance constraint, time-inconsistent preferences induce the agent to hold more risky assets. Intuitively, because of time-inconsistent preferences, the consumer prefers to consume more, and thus might cause the future wealth to decrease. As a result, the consistent performance constraint will tighten at a high probability. In order to mitigate the adverse effect on current self caused by the consistent performance constraint tightening, the consumer has a strong motive to accumulate wealth and hence prefers to increase the allocation of risky asset. It can provide theoretical support for the relationship between the time preference and the risk preference (Dimmock and Kouwenberg,2010; Tavares, 2022; Epper and Fehr-Duda, 2024), and can give better prediction for empirical facts such as investment behaviors in risky assets. Secondly, given the degree of consistent-performance constraint, time-inconsistent preferences cause consumption-benchmark wealth ratio to decline. On the one hand, time-inconsistent preferences can cause the consumption to increase. On the other hand, the consistent performance causes the consumption to decrease and the benchmark wealth level to increase. The interaction effects on consumption and wealth decrease the consumption-benchmark wealth ratio. Lastly, with the consistent performance constraint, the time-inconsistent preferences reduce the marginal propensity of consumption out of wealth, and thus reduce the wealth effect on consumption. The theoretical model in this paper subsequently provides better prediction for existing financial wealth effect on consumption in empirical data.

Key words: Time-inconsistent preference, consistent performance, consumption, risky asset