Good deal bounds with convex constraints

TL;DR

This paper explores the structure of good deal bounds within convex constrained financial markets, extending existing theories by characterizing bounds through convex risk measures called good deal valuations.

Contribution

It introduces the concept of good deal valuations for convex constrained markets and analyzes their properties, extending the Fundamental Theorem of Asset Pricing.

Findings

Good deal bounds are characterized by convex risk measures.

The paper establishes properties of good deal valuations.

Connections to superhedging costs and fundamental theorems are discussed.

Abstract

We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a good deal bound are naturally described by a convex risk measure. We call such a risk measure a good deal valuation; and study its properties. We also discuss superhedging cost and Fundamental Theorem of Asset Pricing for convex constrained markets.