Enlargement of Filtration with Finance in View

Aksamit, Anna; Jeanblanc, Monique

doi:10.1007/978-3-319-41255-9

Cited by 127 publications

(117 citation statements)

References 0 publications

Supporting

Mentioning

115

Contrasting

Order By: Relevance

“…where A and a are nondecreasing processes which do not increase on the same sets (that is, dA and da are orthogonal measures) 1 , and a 0 = A 0 = 0. In order to preserve the compatibility with the decomposition result in Theorem 3.4, dA is assumed absolutely continuous with respect to d M Y .…”

Section: A Results On the Existence Of A Supermartingale Measurementioning

confidence: 99%

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

Coculescu

Jeanblanc

2019

Finance Stoch

Self Cite

View full text Add to dashboard Cite

Under short sales prohibitions, no free lunch with vanishing risk (NFLVRS) is known to be equivalent to the existence of an equivalent supermartingale measure for the price processes (Pulido [26]).We give a necessary condition for the drift of a price process to satsify (NFLVRS). For two given price processes, we introduce the concept of fundamental supermartingale measure, and when a certain condition necessary to the construction of this fundamental supermartingale measure is not fulfilled, we provide the corresponding arbitrage portfolios. The motivation of our study lies in understanding the particular case of converging prices, i.e., two prices that coincide at a bounded random time.

show abstract

Section: A Results On the Existence Of A Supermartingale Measurementioning

confidence: 99%

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

Coculescu

Jeanblanc

2019

Finance Stoch

Self Cite

View full text Add to dashboard Cite

show abstract

“…Kusuoka has shown that any G-martingale can be represented as a sum of a stochastic integral with respect to the Brownian motion and a stochastic integral with respect to the compensated G-martingale M (τ ) of the indicator process A := 1 [[τ,∞[[ . Under the hypotheses that the filtration F enjoys the predictable representation property, F is immersed in G, and τ avoids stopping times, this result was extended for a positive Azéma supermartingale Z in Aksamit & Jeanblanc [3,Th. 3.13] and, for the case of an arbitrary supermartingale Z, in Coculescu et al [10].…”

Section: Introductionmentioning

confidence: 94%

Integral representations of martingales for progressive enlargements of filtrations

Aksamit

Jeanblanc

Rutkowski

2019

Stochastic Processes and their Applications

Self Cite

View full text Add to dashboard Cite

We work in the setting of the progressive enlargement G of a reference filtration F through the observation of a random time τ . We study an integral representation property for some classes of G-martingales stopped at τ . In the first part, we focus on the case where F is a Poisson filtration and we establish a predictable representation property with respect to three G-martingales. In the second part, we relax the assumption that F is a Poisson filtration and we assume that τ is an F-pseudo-stopping time. We establish integral representations with respect to some G-martingales built from F-martingales and, under additional hypotheses, we obtain a predictable representation property with respect to two G-martingales.

show abstract

“…In more recent years many results on insider trading models appeared, we just mention [12,13,14] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Insider information and its relation with the arbitrage condition and the utility maximization problem

D’Auria¹,

Salmerón²

2019

MBE

View full text Add to dashboard Cite

Within the well-known framework of financial portfolio optimization, we analyze the existing relationships between the condition of arbitrage and the utility maximization in presence of insider information. We assume that, since the initial time, the information flow is altered by adding the knowledge of an additional random variable including future information. In this context we study the utility maximization problem under the logarithmic and the Constant Relative Risk Aversion (CRRA) utilities, with and without the restriction of no temporary-bankruptcy.In particular, we show that the value of the insider information may be bounded while the arbitrage condition holds and we prove that the insider information does not always imply arbitrage for the insider by providing an explicit example.T 0 Θ T t σ(t, S t ) 2 dt < +∞ almost surely. When T = F, we suppress the superscript notation.

show abstract

Enlargement of Filtration with Finance in View

Cited by 127 publications

References 0 publications

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

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

Integral representations of martingales for progressive enlargements of filtrations

Insider information and its relation with the arbitrage condition and the utility maximization problem

Contact Info

Product

Resources

About