Related papers: The Entropic Measure Transform
Partial Differential Equations (PDEs) are fundamental for modeling physical systems, yet solving them in a generic and efficient manner using machine learning-based approaches remains challenging due to limited multi-input and multi-scale…
The set of solutions inferred by the generic maximum entropy (MaxEnt) or maximum relative entropy (MaxREnt) principles of Jaynes - considered as a function of the moment constraints or their conjugate Lagrangian multipliers - is endowed…
We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability…
This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has…
In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…
Entropy based ideas find wide-ranging applications in finance for calibrating models of portfolio risk as well as options pricing. The abstracted problem, extensively studied in the literature, corresponds to finding a probability measure…
We make use of an entropic property to establish a convergence theorem (Main Theorem), which reveals that the conditional entropy measures the asymptotic Gaussianity. As an application, we establish the {\it entropic conditional central…
In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal…
The aim of this note is to introduce a notion of dynamical entropy, which we call infinite-product entropy, for probability measures on (countable) infinite cartesian product of any measurable space with itself. The idea behind the…
Let $\Lambda$ be a complex manifold and let $(f_\lambda)_{\lambda\in \Lambda}$ be a holomorphic family of rational maps of degree $d\geq 2$ of $\mathbb{P}^1$. We define a natural notion of entropy of bifurcation, mimicking the classical…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…
The method of maximum entropy has proven to be a rather powerful way to solve the inverse problem consisting of determining a probability density $f_S(s)$ on $[0,\infty)$ from the knowledge of the expected value of a few generalized…
In electricity markets, it is sensible to use a two-factor model with mean reversion for spot prices. One of the factors is an Ornstein-Uhlenbeck (OU) process driven by a Brownian motion and accounts for the small variations. The other…
In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…
Risk-neutral pricing dictates that the discounted derivative price is a martingale in a measure equivalent to the economic measure. The residual ambiguity for incomplete markets is here resolved by minimising the entropy of the price…
We consider the probability measure minimizing a free energy functional equal to the sum of a Coulomb interaction, a confinement potential and an entropy term, which arises in the statistical mechanics of Coulomb gases. In the limit where…
We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…
The Maximum Entropy Modeling Toolkit supports parameter estimation and prediction for statistical language models in the maximum entropy framework. The maximum entropy framework provides a constructive method for obtaining the unique…
We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility…
We investigate the use of entropy-regularized optimal transport (EOT) cost in developing generative models to learn implicit distributions. Two generative models are proposed. One uses EOT cost directly in an one-shot optimization problem…