Multi-Period Liability Clearing via Convex Optimal Control

TL;DR

This paper formulates the multi-period liability clearing problem as a convex optimal control problem, enabling flexible and efficient solutions for various financial clearing scenarios.

Contribution

It introduces a convex optimal control framework for liability clearing, with adaptable costs and constraints for diverse applications and extensions.

Findings

Convex formulation allows efficient solution of liability clearing.

Flexible cost and constraint structures for different scenarios.

Extensions handle uncertainties, bailouts, and partial clearing.

Abstract

We consider the problem of determining a sequence of payments among a set of entities that clear (if possible) the liabilities among them. We formulate this as an optimal control problem, which is convex when the objective function is, and therefore readily solved. For this optimal control problem, we give a number of useful and interesting convex costs and constraints that can be combined in any way for different applications. We describe a number of extensions, for example to handle unknown changes in cash and liabilities, to allow bailouts, to find the minimum time to clear the liabilities, or to minimize the number of non-cleared liabilities, when fully clearing the liabilities is impossible.