Partial Equilibria with Convex Capital Requirements: Existence, Uniqueness and Stability

TL;DR

This paper studies the existence, uniqueness, and stability of partial equilibrium prices in incomplete financial markets with convex capital requirements, providing theoretical conditions and robustness results.

Contribution

It introduces a framework for analyzing partial equilibria with convex capital requirements, including conditions for existence, uniqueness, and stability of equilibrium prices.

Findings

Existence and uniqueness of equilibrium prices under certain conditions

Equilibrium prices are stable against misspecifications of risk preferences

Provides a theoretical foundation for equilibrium analysis in incomplete markets

Abstract

In an incomplete semimartingale model of a financial market, we consider several risk-averse financial agents who negotiate the price of a bundle of contingent claims. Assuming that the agents' risk preferences are modelled by convex capital requirements, we define and analyze their demand functions and propose a notion of a partial equilibrium price. In addition to sufficient conditions for the existence and uniqueness, we also show that the equilibrium prices are stable with respect to misspecifications of agents' risk preferences.