Convex pricing by a generalized entropy penalty

TL;DR

This paper introduces a convex pricing method for nonattainable claims in incomplete markets, based on a generalized entropy penalty, providing a consistent and interpretable pricing framework.

Contribution

It proposes a novel convex monotonic pricing functional as the convex conjugate of a generalized entropy penalty, extending pricing theory in incomplete markets.

Findings

The pricing functional is compatible with attainable claim prices.

Provides an interpretation in terms of tracking with vanishing risk.

Extends existing entropy-based pricing methods.

Abstract

In an incomplete Brownian-motion market setting, we propose a convex monotonic pricing functional for nonattainable bounded contingent claims which is compatible with prices for attainable claims. The pricing functional is defined as the convex conjugate of a generalized entropy penalty functional and an interpretation in terms of tracking with instantaneously vanishing risk can be given.