A Numerical Approach to the Estimation of the Solutions of some Variational Problems with Convexity Costraints

TL;DR

This paper introduces a numerical algorithm for approximating solutions to variational problems constrained by convexity, with applications in economic models like adverse selection and optimal pricing.

Contribution

It develops a novel numerical method specifically designed for variational problems with convexity constraints, applicable to economic and financial modeling.

Findings

Effective approximation of solutions to convex variational problems.

Application to economic models such as adverse selection and pricing.

Potential for improved computational methods in constrained optimization.

Abstract

We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection problems within a Principal-Agent framework. Problems such as product lines design, optimal taxation, structured derivatives design, etc. can be studied through the scope of these models. We develop a method to estimate their optimal pricing schedules.