No-arbitrage conditions and pricing from discrete-time to continuous-time strategies

TL;DR

This paper introduces a unified framework for continuous-time financial models using simple strategies and topologies that bypass stochastic calculus, establishing equivalences of no-arbitrage conditions between discrete and continuous time.

Contribution

It develops a general approach for continuous-time models from simple strategies, avoiding stochastic calculus, and proves the equivalence of no-arbitrage conditions across discrete and continuous frameworks.

Findings

No-arbitrage conditions in continuous time hold iff they hold in discrete time.

Super-hedging prices are the same in continuous and discrete time without no-arbitrage assumptions.

The framework avoids stochastic calculus and semimartingale models.

Abstract

In this paper, a general framework is developed for continuous-time financial market models defined from simple strategies through conditional topologies that avoid stochastic calculus and do not necessitate semimartingale models. We then compare the usual no-arbitrage conditions of the literature, e.g. the usual no-arbitrage conditions NFL, NFLVR and NUPBR and the recent AIP condition. With appropriate pseudo-distance topologies, we show that they hold in continuous time if and only if they hold in discrete time. Moreover, the super-hedging prices in continuous time coincide with the discrete-time super-hedging prices, even without any no-arbitrage condition.