Working paper

Optimal insurance for time-inconsistent agents

Frédéric Cherbonnier


We examine the provision of insurance against non-observable liquidity shocks for time-inconsistent agents who can privately store resources. When lack of self-control is strong enough, optimal contracts are similar to individual nancial accounts with remunerated savings and costly borrowing. The corresponding rate of return decreases with savings, which gives a theoretical rationale for pension accounts with decreasing incentive schemes, as implemented in most developed countries. Extending the model to an innite horizon, we show that, in the presence of repeated shocks, optimal contracts lead to impoverishment almost surely. Usury laws, capping interest rates, worsen this tendency to over-indebtedness for consumers with low risk aversion. By contrast, hidden storage constrains resource allocation for time-consistent agents, so that optimal contracts induce them to accumulate wealth. Those results show how lack of self-control changes the nature of optimal savings and borrowing instruments, with normative implications in terms of tax policy and credit regulation.


Time-inconsistency; self-control; mechanism design; insurance, over-indebtedness; retirement savings; consumer credit; credit regulation; saving incentives;

JEL codes

  • C61: Optimization Techniques • Programming Models • Dynamic Analysis
  • C63: Computational Techniques • Simulation Modeling
  • C73: Stochastic and Dynamic Games • Evolutionary Games • Repeated Games
  • D82: Asymmetric and Private Information • Mechanism Design
  • E21: Consumption • Saving • Wealth
  • H21: Efficiency • Optimal Taxation

See also

Published in

IAST working paper, n. 21-123, September 2021