Title: A note on Pareto optimality in incomplete markets

Authors: Christos Kountzakis

Addresses: Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, GR-83 200 Samos, Greece

Abstract: The aim of this paper is to show in a detailed way, whether the first welfare theorem is valid in the case of incomplete markets. The first welfare theorem is true, under assumptions that rely on the existence of equilibrium in incomplete markets and its validity is heavily related to differentiability and strict convexity assumptions for the utility functions of the investors. In this paper we show that this frame may be weaker. The assumptions for the utility functions may be weaker and they actually fit the assumptions recently obtained for the existence of equilibrium. However, there is not any exact version of the first welfare theorem, relying on a specific model about utility functions and structure of the markets themselves. This fact actually makes our paper significant.

Keywords: incomplete markets; welfare in incomplete markets; no-arbitrage; effectively complete markets.

DOI: 10.1504/IJFMD.2025.151611

International Journal of Financial Markets and Derivatives, 2025 Vol.10 No.2, pp.129 - 134

Received: 30 Dec 2023
Accepted: 28 Jan 2025
Published online: 10 Feb 2026 *

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