Related papers: Representation for martingales living after a rand…
In this paper, we consider the discrete-time setting, and the market model described by (S,F,T)$. Herein F is the ``public" flow of information which is available to all agents overtime, S is the discounted price process of d-tradable…
Financial markets provide an ideal frame for the study of crossing or first-passage time events of non-Gaussian correlated dynamics mainly because large data sets are available. Tick-by-tick data of six futures markets are herein considered…
In this paper we explain that the natural filtration of a continuous Hunt process is continuous, and show that martingales over such a filtration are continuous. We further establish a martingale representation theorem for a class of…
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…
Invariance times are stopping times $\tau$ such that local martingales with respect to some reduced filtration and an equivalently changed probability measure, stopped before $\tau$ , are local martingales with respect to the original model…
In stochastic analysis, the flow of information through time is typically modelled using a filtration. We introduce some of the basic ideas involving enlargements of filtration. Here, we focus mainly on initial enlargements, where a given…
We present two examples of loss of the predictable representation property for semi-martingales by enlargement of the reference filtration. First of all we show that the predictable representation property for a square-integrable…
This work is concerned with the theory of initial and progressive enlargements of a reference filtration F with a random time {\tau}. We provide, under an equivalence assumption, slightly stronger than the absolute continuity assumption of…
In this paper we extend the notion of ``filtration-consistent nonlinear expectation" (or "${\cal F}$-consistent nonlinear expectation") to the case when it is allowed to be dominated by a $g$-expectation that may have a quadratic growth. We…
Given two filtrations $\mathbb F \subset \mathbb G$, we study under which conditions the $\mathbb F$-optional projection and the $\mathbb F$-dual optional projection coincide for the class of $\mathbb G$-optional processes with integrable…
Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of…
This paper considers the nonlinear theory of G-martingales as introduced by Peng. A martingale representation theorem for this theory is proved by using the techniques and the results established in an accompanying paper for the second…
We show that all local martingales with respect to the initially enlarged natural filtration of a vector of multivariate point processes can be weakly represented up to the minimum among the explosion times of the components. We also prove…
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…
We consider the problem of learning two families of time-evolving random measures from indirect observations. In the first model, the signal is a Fleming--Viot diffusion, which is reversible with respect to the law of a Dirichlet process,…
Survival analysis, or time-to-event modelling, is a classical statistical problem that has garnered a lot of interest for its practical use in epidemiology, demographics or actuarial sciences. Recent advances on the subject from the point…
A general diffusion semimartingale is a one-dimensional path-continuous semimartingale that is also a regular strong Markov process. We say that a continuous semimartingale has the representation property if all local martingales w.r.t. its…
We introduce simplicial persistence, a measure of time evolution of network motifs in subsequent temporal layers. We observe long memory in the evolution of structures from correlation filtering, with a two regime power law decay in the…
We show that, under certain smoothness conditions, a Brownian martingale, when evaluated at a fixed time, can be represented via an exponential formula at a later time. The time-dependent generator of this exponential operator only depends…
The paper studies thin times which are random times whose graph is contained in a countable union of the graphs of stopping times with respect to a reference filtration $\mathbb F$. We show that a generic random time can be decomposed into…