The Deterministic and Stochastic Shallow Lake Problem

TL;DR

This paper analyzes the welfare function in both deterministic and stochastic shallow lake problems, demonstrating it as a viscosity solution to the Bellman equation and providing properties and numerical methods.

Contribution

It introduces a rigorous analysis of the welfare function as a viscosity solution and develops a convergent numerical scheme for the shallow lake problem.

Findings

Welfare function characterized as viscosity solution

Asymptotic behavior at infinity established

A convergent monotone numerical scheme developed

Abstract

We study the welfare function of the deterministic and stochastic shallow lake problem. We show that the welfare function is the viscosity solution of the associated Bellman equation, we establish several properties including its asymptotic behaviour at infinity and we present a convergent monotone numerical scheme.