Related papers: Martingale Representation Theorem for the G-expect…

We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…

We present a new approach to noncommutative stochastic calculus that is, like the classical theory, based primarily on the martingale property. Using this approach, we introduce a general theory of stochastic integration and quadratic…

This paper introduces Martingales by covering introductory measure theory concepts and the Lebesgue Integration and Conditional Expectation. It follows up with proofs of Kolomorgov's Theorem on conditional expectations, the Martingale…

In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…

We represent an exchange economy in terms of statistical ensembles for complex networks by introducing the concept of market configuration. This is defined as a sequence of nonnegative discrete random variables $\{w_{ij}\}$ describing the…

The purpose of this note is to propose a new approach for the probabilistic interpretation of Hamilton-Jacobi-Bellman equations associated with stochastic recursive optimal control problems, utilizing the representation theorem for…

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…

We give a pedagogical introduction of the stochastic variational method by considering the quantization of a non-inertial particle system. We show that the effects of fictitious forces are represented in the forms of vector fields which…

The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…

Estimating individual-level treatment effect from observational data is a fundamental problem in causal inference and has attracted increasing attention in the fields of education, healthcare, and public policy.In this work, we concentrate…

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and…

In the paper a problem of risk measures on a discrete-time market model with transaction costs is studied. Strategy effectiveness and shortfall risk is introduced. This paper is a generalization of quantile hedging presented in [4].

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…

We give error estimates in Peng's central limit theorem for not necessarily nondegenerate case. The exposition uses the language of the classical probability theory instead of the language of the theory of sublinear expectations. We only…

In this note we define and study the stochastic process $X$ in link with a parabolic transmission operator $(A,D(A))$ in divergence form. The transmission operator involves a diffraction condition along a transmission boundary. To that aim…

We work in the setting of the progressive enlargement $\mathbb G$ of a reference filtration $\mathbb F$ through the observation of a random time $\tau$. We study an integral representation property for some classes of $\mathbb…

Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range…

Complementing the analysis in [41], we investigate the well-posedness of SPDEs problems of doubly nonlinear type. These arise ubiquitously in the modelization of dissipative media and correspond to generalized balance laws between…

Many applications require stochastic processes specified on two- or higher-dimensional domains; spatial or spatial-temporal modelling, for example. In these applications it is attractive, for conceptual simplicity and computational…

Kramkov and Sirbu (2006, 2007) have shown that first-order approximations of power utility-based prices and hedging strategies can be computed by solving a mean-variance hedging problem under a specific equivalent martingale measure and…