相关论文: Martingale representation processes and applicatio…
We consider a viable market model. Suppose that new information arrives at the market. We are interested in modeling the market reaction facing to the change of information. In particular we seek for the limit on the intensity of…
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…
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…
The information dynamics in finance and insurance applications is usually modeled by a filtration. This paper looks at situations where information restrictions apply such that the information dynamics may become non-monotone. A fundamental…
We give a bare-hands approach to the martingale representation theorem for integer valued random measures, which allows for a wide class of infinite activity jump processes, as well as all processes with well-ordered jumps.
This paper introduces a martingale that characterizes two properties of evolving forecast distributions. Ideal forecasts of a future event behave as martingales, sequen- tially updating the forecast to leverage the available information as…
We propose \textit{DeepMartingale}, a deep-learning framework for the dual formulation of discrete-monitoring optimal stopping problems under continuous-time models. Leveraging a martingale representation, our method implements a…
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 a market model where there are two levels of information. The public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can…
New proofs are given of the existence of the compensator (or dual predictable projection) of a locally integrable c\'adl\'ag adapted process of finite variation and of the existence of the quadratic variation process for a c\'adl\'ag local…
In a fully general setting, we study the relation between martingale spaces under two locally absolutely continuous probabilities and prove that the martingale representation property (MRP) is always stable under locally absolutely…
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…
We consider a financial market model with a single risky asset whose price process evolves according to a general jump-diffusion with locally bounded coefficients and where market participants have only access to a partial information flow.…
Our financial setting consists of a market model with two flows of information. The smallest flow F is the "public" flow of information which is available to all agents, while the larger flow G has additional information about the…
Given a real valued and time-inhomogeneous martingale diffusion X, we investigate the properties of functions defined by the conditional expectation f(t,X_t)=E[g(X_T)|F_t]. We show that whenever g is monotonic or Lipschitz continuous then…
We discuss martingales, detrending data, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that Martingale stochastic…
Let X and Y be an m-dimensional F-semimartingale and an n-dimensional H-semimartingale respectively on the same probability space, both enjoying the strong predictable representation property. We propose a martingale representation result…
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…
Consider $\mathbb{G}$ the progressive enlargement of a filtration $\mathbb{F}$ with a random time $\tau$. Assuming that, in $\mathbb{F}$, the martingale representation property holds, we examine conditions under which the martingale…
For a general Multidimensional L\'{e}vy process (satisfying some moment conditions), we introduce the Multidimensional power jump processes and the related Multidimensional Teugels martingales. Furthermore, we orthogonalize the…