Risk Arbitrage and Hedging to Acceptability under Transaction Costs

TL;DR

This paper extends classical models of transaction costs by incorporating convex costs and acceptable positions, analyzing superhedging prices and arbitrage conditions under these generalized settings.

Contribution

It introduces a framework combining convex transaction costs with risk-based acceptable positions, expanding the classical no arbitrage theory to more realistic market models.

Findings

Superhedging prices decrease with risk considerations.

Stronger no arbitrage conditions are identified in the generalized setting.

Connections to no good deals framework are established.

Abstract

The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction costs and assuming that increments of the portfolio process belong to the sum of a solvency set and a family of multivariate acceptable positions, e.g. with respect to a dynamic risk measure. We describe the sets of superhedging prices, formulate several no (risk) arbitrage conditions and explore connections between them. In the special case when multivariate positions are converted into a single fixed asset, our framework turns into the no good deals setting. However, in general, the possibilities of assessing the risk with respect to any asset or a basket of the assets lead to a decrease of superhedging prices and the no arbitrage conditions become stronger. The mathematical technique relies on results for unbounded and possibly non-closed random sets in Euclidean space.