In this paper we analyze a stochastic continuous time model in finite horizon in which the agent discounts the instantaneous utility function and the final function at constant but different instantaneous discount rates of time preference. Within this context we can model problems in which, when...

Dybvig [1995] finds optimal spending and investment strategies for a perpetual endowment that has no tolerance for spending declines. His spending rule is a ratchet --- spending never decreases, but has a substantial chance of increasing. We find the ratchet consumption rule for an investor with...

We combine forward investment performance processes and ambiguity averse portfolio selection. We introduce the notion of robust forward criteria which addresses the issues of ambiguity in model specification and in preferences and investment horizon specification. It describes the evolution of...

This paper examines an Epstein-Zin recursive utility with quasi-hyperbolic discounting in continuous time. I directly define the utility process and consider a Merton's optimal consumption-investment problem for application. I show that a solution to the Hamilton-Jacobi-Bellman equation is the...

For time inconsistent multi-period mean-variance portfolio decision, we develop a two-tier planner-doer game model with self-control, in which planner and doers represent different interests of the same investor at different time instants and planner (the willpower to resist short term...

In this paper, we continue our study on a general time-inconsistent stochastic linear-quadratic (LQ) control problem originally formulated in Hu, Jin and Zhou (2012). We derive a necessary and sufficient condition for equilibrium controls via a flow of forward-backward stochastic differential...

Quite recently, a great interest has been devoted to time-consistency of risk measures in its different formulations (see Delbaen, Follmer and Penner, Bion-Nadal, Delbaen et al., Laeven and Stadje, among many others). However, almost all the papers address to coherent or convex risk measures...

When a stochastic decision problem is time inconsistent, the decision maker would always be troubled by his conflicting decisions “optimally” derived from his time-varying preferences at different time instants. The long-run self (LR) of the decision maker pursues the long-term optimality...