Initial Enlargement in a Markov chain market model

TL;DR

This paper investigates how initial enlargement of filtrations affects jump times and arbitrage opportunities in a Markov chain market model, revealing that insider information can alter jump accessibility without necessarily enabling arbitrage.

Contribution

It provides a detailed analysis of initial enlargement effects on jump times and arbitrage in a Markov chain market, extending the understanding of insider information impacts.

Findings

Jump times can become accessible or predictable after enlargement.

Even with changed jump times, arbitrage opportunities may not arise.

The study extends the theory of filtration enlargement in financial models.

Abstract

Enlargement of filtrations is a classical topic in the general theory of stochastic processes. This theory has been applied to stochastic finance in order to analyze models with insider information. In this paper we study initial enlargement in a Markov chain market model, introduced by R. Norberg. In the enlargened filtration several things can happen: some of the jumps times can be accessible or predictable, but in the orginal filtration all the jumps times are totally inaccessible. But even if the jumps times change to accessible or predictable, the insider does not necessarily have arbitrage possibilities.