Dynamic Pareto Optima in Multi-Period Pure-Exchange Economies

TL;DR

This paper develops a recursive framework for identifying dynamic Pareto-optimal allocations in multi-period economies with stochastic endowments, using time-consistent risk measures and comonotonicity principles.

Contribution

It introduces the concept of dynamic Pareto-optimal allocations and provides recursive and closed-form methods for their construction under certain preferences.

Findings

Recursive construction of Pareto optima starting from terminal time.

A comonotone improvement theorem for allocation processes.

Closed-form solutions for distortion-type risk measures.

Abstract

We study a problem of optimal allocation in a discrete-time multi-period pure-exchange economy, where agents have preferences over stochastic endowment processes that are represented by strongly time-consistent dynamic risk measures. We introduce the notion of dynamic Pareto-optimal allocation processes and show that such processes can be constructed recursively starting with the allocation at the terminal time. We further derive a comonotone improvement theorem for allocation processes, and we provide a recursive approach to constructing comonotone dynamic Pareto optima when the agents' preferences are coherent and satisfy a property that we call equidistribution-preserving. In the special case where each agent's dynamic risk measure is of the distortion type, we provide a closed-form characterization of comonotone dynamic Pareto optima. We illustrate our results in a two-period setting.