Drift operator in a viable expansion of information flow

Abstract

A triplet $(\mathbb{P},\mathbb{F},S)$ of a probability measure $\mathbb{P}$, of an information flow $\mathbb{F}=({\mathcal{F}}_t{)}_{t\in {\mathbb{R}}_{+}}$, and of an $\mathbb{F}$ adapted asset process $S$, is a financial market model, only if it is viable. In this paper we are concerned with the preservation of the market viability, when the information flow $\mathbb{F}$ is replaced by a bigger one $\mathbb{G}=({\mathcal{G}}_t{)}_{t\ge 0}$ with ${\mathcal{G}}_t\supset {\mathcal{F}}_t$. Under the assumption of martingale representation property in $(\mathbb{P},\mathbb{F})$, we prove a necessary and sufficient condition for all viable market in $\mathbb{F}$ to remain viable in $\mathbb{G}$.

In the paper arXiv:1207.1662, the viability of information flow expansion is studied with a sufficient condition. This paper considers the same problem and obtains a necessary and sufficient condition. There was a mathematical gap in the previous version of this paper. It is corrected in this version

References in corpus (4)

• On arbitrages arising from honest times
• The Existence of Dominating Local Martingale Measures
• An alternative proof of a result of Takaoka
• Construction of multi-default models with full viability

Cited by in corpus (1)

• Construction of multi-default models with full viability