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 $\mathbb{G}=(\mathcal{G}_t)_{t\geq 0}$ 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 $\mathbb{G}$.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2015
- DOI:
- 10.48550/arXiv.1505.03766
- arXiv:
- arXiv:1505.03766
- Bibcode:
- 2015arXiv150503766S
- Keywords:
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- Mathematics - Probability;
- 60G07;
- 60G44;
- 60G40
- E-Print:
- 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