Hopf-Lax formula for variational problems with non-constant discount
Juan Pablo Rinc\'on-Zapatero
TL;DR
This paper derives a Hopf-Lax formula for variational problems with non-constant discount factors and explores the resulting dynamic programming equation and the regularity of the value function.
Contribution
It introduces a novel Hopf-Lax formula tailored for variational problems with non-constant discount, advancing the theoretical understanding of such problems.
Findings
Derived a Hopf-Lax formula for non-constant discount variational problems
Established a dynamic programming equation for the problem
Analyzed regularity properties of the value function
Abstract
We provide a Hop-Lax formula for variational problems with non-constant discount and deduce a dynamic programming equation. We also study some regularity properties of the value function.
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Taxonomy
TopicsEconomic theories and models · Optimization and Variational Analysis · Decision-Making and Behavioral Economics