Radner equilibrium in incomplete Levy models

TL;DR

This paper develops a continuous-time Radner equilibrium model with Levy process-driven income and dividend streams, providing closed-form solutions and insights into how untradeable income streams affect market risk premiums and interest rates.

Contribution

It introduces a novel equilibrium framework with Levy processes and derives explicit closed-form solutions for prices and rates, highlighting effects of untradeable income streams.

Findings

Equilibrium Sharpe ratio can be increased by Levy jumps.

Equilibrium interest rate can be decreased when income streams are untradeable.

Closed-form solutions facilitate analysis of jump-driven market dynamics.

Abstract

We construct continuous-time equilibrium models based on a finite number of exponential utility investors. The investors' income rates as well as the stock's dividend rate are governed by discontinuous Levy processes. Our main result provides the equilibrium (i.e., bond and stock price dynamics) in closed-form. As an application, we show that the equilibrium Sharpe ratio can be increased and the equilibrium interest rate can be decreased (simultaneously) when the investors' income streams cannot be traded.