No-arbitrage under a class of honest times

@article{Aksamit2018NoarbitrageUA,
  title={No-arbitrage under a class of honest times},
  author={Anna Aksamit and Tahir Choulli and Jun Deng and Monique Jeanblanc},
  journal={Finance and Stochastics},
  year={2018},
  volume={22},
  pages={127-159}
}
This paper quantifies the interplay between the no-arbitrage notion of no unbounded profit with bounded risk (NUPBR) and additional progressive information generated by a random time. This study complements the one of Aksamit et al. (Finance Stoch. 21:1103–1139, 2017) in which the authors have studied similar topics for the model stopped at the random time, while here we deal with the question of what happens after the random time. Given that the existing literature proves that NUPBR is always… Expand
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References

SHOWING 1-10 OF 44 REFERENCES
Non-Arbitrage up to Random Horizon for Semimartingale Models ∗
This paper addresses the question of how an arbitrage-free semimartingale model is affected when stopped at a random horizon. We focus on No-Unbounded-Profit-with-Bounded-Risk (called NUPBRExpand
No-arbitrage up to random horizon for quasi-left-continuous models
TLDR
The impact of stopping the price process at an arbitrary random time on the condition of no unbounded profit with bounded risk (called NUPBR), also known in the literature as no arbitrage of the first kind, is studied. Expand
On arbitrages arising with honest times
TLDR
It is explicitly shown that no kind of arbitrage profit can ever be realised strictly before τ, whereas classical arbitrage opportunities can be realised exactly at τ as well as after τ. Expand
Arbitrages in a Progressive Enlargement Setting
This paper completes the analysis of Choulli et al. Non-Arbitrage up to Random Horizons and after Honest Times for Semimartingale Models and contains two principal contributions. The firstExpand
How non-arbitrage, viability and numéraire portfolio are related
This paper proposes two approaches that quantify the exact relationship among viability, absence of arbitrage, and/or existence of the numéraire portfolio under minimal assumptions and for generalExpand
ESSAYS ON ARBITRAGE THEORY FOR A CLASS OF INFORMATIONAL MARKETS
This thesis develops three major essays on Arbitrage Theory, Market’s Viability and Informational Markets. The first essay (Chapter 3) elaborates the exact connections among theExpand
A note on the condition of no unbounded profit with bounded risk
TLDR
It is proved, in a general finite-dimensional semimartingale setting, that the no unbounded profit with bounded risk (NUPBR) condition is equivalent to the existence of a strict sigma-martingale density. Expand
Random times at which insiders can have free lunches
We consider models of time continuous financial markets with a regular trader and an insider who are able to invest into one risky asset. The insider's additional knowledge consists in his ability toExpand
Minimal Hellinger martingale measures of order q
TLDR
This paper shows the existence of the MHM measure of order q and describes it explicitly in terms of pointwise equations in ℝd and proves that, for an agent to be indifferent with respect to the liquidation time of her assets, she is forced to consider a habit formation utility function instead of the original utility. Expand
Study of a Filtration Expanded to Include an Honest Time
This paper presents a martingale approach to work on the decomposition of a process into its 'past ' and 'future' relative to an honest random time. (See Millar 1-11], for a survey of the MarkovianExpand
...
1
2
3
4
5
...