Consumption-investment decisions with endogenous reference point and drawdown constraint

We study a consumption-investment decision problem related to the past spending maximum. In problem, we consider two crucial consumption levels: lowest constrained level and reference level, both levels are fractions of The decision-maker has different risk aversions on sides level. solve this stochastic control derive semi-explicit forms value function, optimal plan, investment strategy. find five important wealth thresholds which nonlinear functions Based numerical results theoretical analysis, also that model significant economic implications. There at least three predictions: marginal propensity consume out is generally decreasing but can be increasing for intermediate levels, it varies inversely with aversion level; implied relative roughly smile in wealth; welfare much more vulnerable shocks when not reached.