# Optional projection under equivalent local martingale measures

@article{Biagini2020OptionalPU, title={Optional projection under equivalent local martingale measures}, author={Francesca Biagini and Andrea Mazzon and Ari-Pekka Perkkio}, journal={arXiv: Mathematical Finance}, year={2020} }

Motivation for this paper is to understand the impact of information on asset price bubbles and perceived arbitrage opportunities. This boils down to study optional projections of $\mathbb{G}$-adapted strict local martingales into a smaller filtration $\mathbb{F}$ under equivalent martingale measures. We give some general results as well as analyze in details two specific examples given by the inverse three dimensional Bessel process and a class of stochastic volatility models.

## 2 Citations

Filtration shrinkage, the structure of deflators, and failure of market completeness

- Mathematics
- 2020

We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part in the multiplicative Doob-Meyer…

Filtration Shrinkage, the Structure of Deflators, and Failure of Market Completeness

- MathematicsSSRN Electronic Journal
- 2019

We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part in the multiplicative Doob-Meyer…

## References

SHOWING 1-10 OF 44 REFERENCES

Complications with stochastic volatility models

- Mathematics, EconomicsAdvances in Applied Probability
- 1998

We show a class of stock price models with stochastic volatility for which the most natural candidates for martingale measures are only strictly local martingale measures, contrary to what is usually…

Local martingales and filtration shrinkage

- Mathematics
- 2011

A general theory is developed for the projection of martingale related processes onto smaller filtrations, to which they are not even adapted. Martingales, supermartingales, and semimartingales…

Local martingales, bubbles and option prices

- Mathematics, EconomicsFinance Stochastics
- 2005

It turns out that the option value depends critically on the definition of admissible strategy, and that the standard mathematical definition may not be consistent with the definitions used for trading.

Some no-arbitrage rules under short-sales constraints, and applications to converging asset prices

- MathematicsFinance Stochastics
- 2019

This study gives a necessary condition for the drift of a price process to satisfy NFLVRS, and when a certain condition necessary for the construction of this fundamental supermartingale measure is not fulfilled, it provides the corresponding arbitrage portfolios.

The Dalang–Morton–Willinger Theorem Under Delayed and Restricted Information

- Mathematics
- 2006

We extend the classical no-arbitrage criteria to the case of a model where the investor’s decisions are based on a partial information (e.g., because of delay or round-off errors), that is the…

Filtration shrinkage, strict local martingales and the Follmer measure

- Mathematics
- 2014

When a strict local martingale is projected onto a subfiltration to which it is not adapted, the local martingale property may be lost, and the finite variation part of the projection may have…

ARBITRAGE AND FREE LUNCH WITH BOUNDED RISK FOR UNBOUNDED CONTINUOUS PROCESSES

- Mathematics
- 1994

We give two examples showing that for unbounded continuous price processes, the no-free-lunch assumption and the existence of an equivalent martingale measure are not equivalent. In fact it turns out…

Modeling Credit Risk with Partial Information

- Economics
- 2004

This paper provides an alternative approach to Duffie and Lando (2001) for obtaining a reduced form credit risk model from a structural model. Duffie and Lando obtain a reduced form model by…

ASSET PRICE BUBBLES IN INCOMPLETE MARKETS *

- Economics
- 2008

This paper studies asset price bubbles in a continuous time model using the local martingale framework. Providing careful definitions of the asset's market and fundamental price, we characterize all…