Related papers: Kullback-Leibler cluster entropy to quantify volat…
Experimental designs are tools which can drastically reduce the number of simulations required by time-consuming computer codes. One strategy for selecting the values of the inputs, whose response is to be observed, is to choose these…
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…
Motivated by empirical evidence from the joint behavior of realized volatility time series, we propose to model the joint dynamics of log-volatilities using a multivariate fractional Ornstein-Uhlenbeck process. This model is a multivariate…
This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle, which is used as a probabilistic learning algorithm. This permits the effective integration of data into…
Wide conditions are provided to guarantee asymptotic unbiasedness and L^2-consistency of the introduced estimates of the Kullback-Leibler divergence for probability measures in R^d having densities w.r.t. the Lebesgue measure. These…
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution…
A generalized Kullback-Leibler relative entropy is introduced starting with the symmetric Jackson derivative of the generalized overlap between two probability distributions. The generalization retains much of the structure possessed by the…
In the past few decades considerable effort has been expended in characterizing and modeling financial time series. A number of stylized facts have been identified, and volatility clustering or the tendency toward persistence has emerged as…
This paper focuses on a dynamic multi-asset mean-variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and…
This note outlines a method for clustering time series based on a statistical model in which volatility shifts at unobserved change-points. The model accommodates some classical stylized features of returns and its relation to GARCH is…
We show that the moment generating function of the Kullback-Leibler divergence (relative entropy) between the empirical distribution of $n$ independent samples from a distribution $P$ over a finite alphabet of size $k$ (i.e. a multinomial…
Purpose: This study introduces a novel framework for identifying and exploiting predictive lead-lag relationships in financial markets. We propose an integrated approach that combines advanced statistical methodologies with machine learning…
In the stochastic volatility models for multivariate daily stock returns, it has been found that the estimates of parameters become unstable as the dimension of returns increases. To solve this problem, we focus on the factor structure of…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
Risk contributions of portfolios form an indispensable part of risk adjusted performance measurement. The risk contribution of a portfolio, e.g., in the Euler or Aumann-Shapley framework, is given by the partial derivatives of a risk…
This paper introduces a comprehensive framework for Financial Information Theory by applying information-theoretic concepts such as entropy, Kullback-Leibler divergence, mutual information, normalized mutual information, and transfer…
In this article we study the dependence degree of the traded volume of the Dow Jones 30 constituent equities by using a nonextensive generalised form of the Kullback-Leibler information measure. Our results show a slow decay of the…
We study the worst-case probability that $Y$ outperforms a benchmark $X$ when the law of $Y$ lies in a Kullback-Leibler neighbourhood of the benchmark. The max-min problem over couplings admits a tractable dual (via optimal transport),…
For quantitative trading risk management purposes, we present a novel idea: the realized local volatility surface. Concisely, it stands for the conditional expected volatility when sudden market behaviors of the underlying occur. One is…
We prove characterization theorems for relative entropy (also known as Kullback-Leibler divergence), q-logarithmic entropy (also known as Tsallis entropy), and q-logarithmic relative entropy. All three have been characterized axiomatically…