Fundamental theorem of asset pricing with acceptable risk in markets with frictions

TL;DR

This paper extends the Fundamental Theorem of Asset Pricing to markets with frictions, nonproportional costs, and constraints, characterizing prices consistent with acceptable risk and the absence of scalable good deals.

Contribution

It provides a dual characterization of market-consistent prices with acceptable risk, introducing the concept of scalable good deals in markets with frictions.

Findings

Dual description of prices with acceptable risk

Extension of classical FTAP to include good deals

Highlighting the role of scalable good deals

Abstract

We study the range of prices at which a rational agent should contemplate transacting a financial contract outside a given securities market. Trading is subject to nonproportional transaction costs and portfolio constraints and full replication by way of market instruments is not always possible. Rationality is defined in terms of consistency with market prices and acceptable risk thresholds. We obtain a direct and a dual description of market-consistent prices with acceptable risk. The dual characterization requires an appropriate extension of the classical Fundamental Theorem of Asset Pricing where the role of arbitrage opportunities is played by good deals, i.e., costless investment opportunities with acceptable risk-reward tradeoff. In particular, we highlight the importance of scalable good deals, i.e., investment opportunities that are good deals regardless of their volume.