Related papers: Minimum R\'enyi Entropy Portfolios
Shannon and Renyi entropies are quantitative measures of uncertainty in a data set. They are developed by Renyi in the context of entropy theory. These measures have been studied in the case of the multivariate t-distributions. We extend…
In this paper, we consider the chance constrained based uncertain portfolio optimization problem in which the uncertain parameters are stochastic in nature. The primary goal of the work is to formulate the uncertain problem into a…
Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…
This article studies the fundamental problem of using i.i.d. coin tosses from an entropy source to efficiently generate random variables $X_i \sim P_i$ $(i \ge 1)$, where $(P_1, P_2, \dots)$ is a random sequence of rational discrete…
R\'enyi entropy of order \alpha is a general measure of entropy. In this paper we derive estimations for the R\'enyi entropy of the mixture of sources in terms of the entropy of the single sources. These relations allow to compute the…
Shannon entropy is the shortest average codeword length a lossless compressor can achieve by encoding i.i.d. symbols. However, there are cases in which the objective is to minimize the \textit{exponential} average codeword length, i.e. when…
We propose a novel model to achieve superior out-of-sample Sharpe ratios. While most research in asset allocation focuses on estimating the return vector and covariance matrix, the first component of our novel model instead forecasts the…
In the world of modern financial theory, portfolio construction has traditionally operated under at least one of two central assumptions: the constraints are derived from a utility function and/or the multivariate probability distribution…
This paper gives improved R\'{e}nyi entropy power inequalities (R-EPIs). Consider a sum $S_n = \sum_{k=1}^n X_k$ of $n$ independent continuous random vectors taking values on $\mathbb{R}^d$, and let $\alpha \in [1, \infty]$. An R-EPI…
We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…
In this paper we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense…
The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
In this paper, I expand Shannon's definition of entropy into a new form of entropy that allows integration of information from different random events. Shannon's notion of entropy is a special case of my more general definition of entropy.…
In the market place, diversification reduces risk and provides protection against extreme events by ensuring that one is not overly exposed to individual occurrences. We argue that diversification is best measured by characteristics of the…
The Renyi entropy is a generalisation of the Shannon entropy that is sensitive to the fine details of a probability distribution. We present results for the Renyi entropy of the totally asymmetric exclusion process (TASEP). We calculate…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
We leverage the Gibbs inequality and its natural generalization to R\'enyi entropies to derive closed-form parametric expressions of the optimal lower bounds of $\rho$th-order guessing entropy (guessing moment) of a secret taking values on…
Quantum key distribution requires tight and reliable bounds on the secret key rate to ensure robust security. This is particularly so for the regime of finite block sizes, where the optimization of generalized R\'enyi entropic quantities is…
We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution…