No Arbitrage Conditions For Simple Trading Strategies

TL;DR

This paper investigates conditions under which simple trading strategies do not admit arbitrage opportunities in markets modeled by strict local martingales, extending previous results and including short-sale restrictions.

Contribution

It establishes that the strong Markov property ensures no arbitrage for certain non-negative strict local martingales, generalizing prior results on Bessel processes.

Findings

Strong Markov property implies no arbitrage for certain strict local martingales.

Provides no arbitrage conditions with short-sale restrictions.

Extends previous results on Bessel processes to broader classes of processes.

Abstract

Strict local martingales may admit arbitrage opportunities with respect to the class of simple trading strategies. (Since there is no possibility of using doubling strategies in this framework, the losses are not assumed to be bounded from below.) We show that for a class of non-negative strict local martingales, the strong Markov property implies the no arbitrage property with respect to the class of simple trading strategies. This result can be seen as a generalization of a similar result on three dimensional Bessel process in [3]. We also pro- vide no arbitrage conditions for stochastic processes within the class of simple trading strategies with shortsale restriction.