Permanently locked-in consumption makes investors more cautious, study finds

A new theoretical study in Advances in Continuous and Discrete Models examines what happens when that assumption is removed. Junkee Jeon and Takwon Kim analyze an agent with a finite planning horizon who may raise consumption at any time but can never reduce it, and who must keep consuming at whatever level has been reached even after the planning date ends, for the rest of a life that ends at a random time.

The model is well defined whenever initial wealth is large enough to support the current consumption floor indefinitely. Using duality theory in complete markets, the authors decompose the problem into a continuum of optimal stopping problems through a layer-cake representation. The dual problem, they show, can be interpreted in terms of American put option pricing on the shadow price process, with a strike determined by the relation between the risk-free rate and the effective discount rate.

This mathematical structure yields a concrete characterization of optimal behavior. The optimal consumption policy is described by a free boundary driven by the shadow price, and the wealth-to-consumption ratio is reflected at an endogenous boundary. In practical terms, the optimal consumption policy is characterized through a free boundary driven by the shadow price, and the wealth-to-consumption ratio is reflected at an endogenous boundary determined within the model rather than imposed from outside.

The central finding concerns what the authors call the lifetime lock-in effect. Because any increase in consumption before the terminal date also raises the permanently committed consumption level afterward, each upward adjustment carries an additional cost that a standard finite-horizon ratcheting model does not capture. The result is that the agent behaves more cautiously: upward consumption adjustments occur less frequently, and the optimal risky share is uniformly lower for any given wealth-to-consumption ratio than in the standard model without perpetual commitment.

The work is a theoretical contribution, deriving optimal policies and their characterizations rather than estimating behavior from data. Its value lies in making precise how a commitment that extends beyond the planning horizon changes the entire consumption and investment path while the horizon is still running. By linking the problem to American put option pricing on the shadow price process, the framework connects the consumption problem to a familiar tool from financial mathematics.

Subject of Research: Optimal consumption and investment under a finite-horizon ratcheting constraint with perpetual post-horizon commitment

Article Title: Finite-horizon ratcheting with perpetual commitment: optimal consumption, investment, and lock-in effects

Article References: Jeon, J., & Kim, T. (2026). Finite-horizon ratcheting with perpetual commitment: optimal consumption, investment, and lock-in effects. Advances in Continuous and Discrete Models. https://doi.org/10.1186/s13662-026-04127-7

Image Credits: AI Generated

DOI: 10.1186/s13662-026-04127-7

Keywords: consumption ratcheting, optimal investment, perpetual commitment, lock-in effect, duality theory, optimal stopping, American put option, shadow price, free boundary, wealth-to-consumption ratio, precautionary behavior, finite planning horizon