Large Platonic Markets with Delays

TL;DR

This paper develops a stochastic framework for modeling delays in large financial markets with infinitely many assets, analyzing information and execution delays, and establishing fundamental asset pricing theorems under these conditions.

Contribution

It introduces a novel approach to incorporate random, inhomogeneous delays into large market models and proves the inheritance of no arbitrage conditions under these delays.

Findings

Delayed markets satisfy a fundamental theorem of asset pricing.

Inheritance of no asymptotic Lp-free lunch condition under delays.

Framework accommodates multiple brokers with different trading speeds.

Abstract

The objective is to develop a general stochastic approach to delays on financial markets. We suggest such a concept in the context of large platonic markets, which allow infinitely many assets and incorporate a restricted information setting. The discussion is divided into information delays and order execution delays. The former enables modelling of markets where the observed information is delayed, while the latter provides the opportunity to defer the indexed time of a received asset price. Both delays may be designed randomly and inhomogeneously over time. We show that delayed markets are equipped with a fundamental theorem of asset pricing and our main result is inheritance of the no asymptotic Lp-free lunch condition under both delay types. Eventually, we suggest an approach to verify absence of Lp-free lunch on markets with multiple brokers endowed with deviating trading speeds.