Savings behavior with imperfect capital markets: When hyperbolic discounting leads to discontinuous strategies

► A life-cycle model of consumption with quasi-hyperbolic discounting and imperfect capital market is studied. ► We show the existence of non-convexities that may imply discontinuous equilibrium strategies. ► We give a complete characterization of savings behavior. ► The savings function undergoes jumps and non-monotonicities when the incomes or the interest rates reach threshold values.