Periodic portfolio selection with quasi-hyperbolic discounting

TL;DR

This paper studies an infinite-horizon portfolio optimization problem with agents exhibiting present bias and preference for immediate rewards, analyzing how these biases influence optimal strategies and risk behaviors.

Contribution

It introduces a novel continuous-time model incorporating quasi-hyperbolic discounting and characterizes optimal strategies for different types of agents, including sophisticated planning via mean field games.

Findings

Present bias and naivety do not always reduce risk-taking.

Sophistication can lead to excessive leverage or underinvestment.

Optimal strategies depend on agent type and preference structure.

Abstract

We introduce an infinite-horizon, continuous-time portfolio selection problem faced by an agent with periodic S-shaped preference and present bias. The inclusion of a quasi-hyperbolic discount function leads to time-inconsistency and we characterize the optimal portfolio for a pre-committing, naive and sophisticated agent respectively. In the more theoretically challenging problem with a sophisticated agent, the time-consistent planning strategy can be formulated as an equilibrium to a static mean field game. Interestingly, present bias and naivety do not necessarily result in less desirable risk taking behaviors, while agent's sophistication may lead to excessive leverage (underinvestement) in the bad (good) states of the world.