Arbitrage and utility maximization in market models with an insider

TL;DR

This paper investigates arbitrage opportunities and utility maximization in market models with insider information, providing criteria for market viability, characterizing arbitrage strategies, and establishing duality results for insiders.

Contribution

It introduces new criteria for no unbounded profits with bounded risk in insider markets and characterizes optimal arbitrage strategies with duality results.

Findings

Markets can satisfy NUPBR yet admit arbitrage with insider info.

Criteria for NUPBR in insider markets are established.

Duality results for insider utility maximization are proved.

Abstract

We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses from the beginning an additional information in the form of a random variable G, which only becomes known to the ordinary agents at date T, we give criteria for the No Unbounded Profits with Bounded Risk property to hold, characterize optimal arbitrage strategies, and prove duality results for the utility maximization problem faced by the insider. Examples of markets satisfying NUPBR yet admitting arbitrage opportunities are provided for both atomic and continuous random variables G.