Torben M. Andersen、Joydeep Bhattacharya、 刘盼（通讯作者）, “Commitment and partial naïveté: Early withdrawal penalties on retirement accounts”, Journal of Mathematical Economics (ABS3), published in May 2023, https://doi.org/10.1016/j.jmateco.2023.102844

        Abstract: We analyze a portfolio allocation problem in a standard model of conflict within temporal selves who suffer from partial naïveté – the current self holds a deterministic but possibly wrong perception (underestimation) about the present bias of her future selves. The current self can invest in a liquid and a longer-maturity, illiquid asset; the latter offers partial commitment since the future self may prematurely liquidate it at a penalty rate. If the cost is prohibitive, no liquidation happens, and the first-best plan laid out by the current self is followed. When such costs are modest, raising them has countervailing income and substitution effects. Consequently, in a range, a strengthening of the commitment device of illiquidity is not necessarily welfare increasing for the current self.