Paper: arXiv 2410.18240

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper involves advanced continuous-time stochastic control, mean-field games, and path-dependent optimization with heavy mathematical derivations and theoretical characterizations, but contains no empirical data, backtests, or implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal: Characterize optimal portfolios for<br>agents with present bias and S-shaped preferences"] --> B{"Model Setup"}
  
  B --> C["Inputs: Quasi-hyperbolic discount factor, S-shaped utility, Brownian motion"]
  C --> D["Process: Infinite-horizon continuous-time<br>portfolio selection problem"]
  
  D --> E{"Agent Type"}
  
  E --> F["Pre-committing: Direct optimization"]
  E --> G["Naive: Myopic planning"]
  E --> H["Sophisticated: Mean field game equilibrium"]
  
  F & G & H --> I["Key Findings:<br>- Present bias ≠ necessarily riskier behavior<br>- Sophistication → excessive leverage in bad states<br>- Naivety can lead to overinvestment in good states"]

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