Related papers: Relative and Discrete Utility Maximising Entropy
In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution $p_i$ by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. The…
We study expected utility maximization problem with constant relative risk aversion utility function in a complete market under the reinforcement learning framework. To induce exploration, we introduce the Tsallis entropy regularizer, which…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
Various properties of relative entropy have led to its widespread use in information theory. These properties suggest that relative entropy has a role to play in systems that attempt to perform inference in terms of probability…
Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
In this paper we recall for physicists how it is possible, using the principle of maximization of the Boltzmann-Shannon entropy, to derive the Burr-Bingh-Maddala (burr12) double power law probability distribution function and its…
We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
Radon-Nikodym (RN) derivative between two measures arises naturally in the affine structure of the space of probability measures with densities. Entropy, free energy, relative entropy, and entropy production as mathematical concepts…
In random expected utility (Gul and Pesendorfer, 2006), the distribution of preferences is uniquely recoverable from random choice. This paper shows through two examples that such uniqueness fails in general if risk preferences are random…
The Renyi entropy coprises a group of data estimates that sums up the well-known Shannon entropy, acquiring a considerable lot of its properties. It appears as unqualified and restrictive entropy, relative entropy, or common data, and has…
A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally…
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the…
We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the…
This paper investigates an optimal consumption-investment problem featuring recursive utility via Tsallis relative entropy. We establish a fundamental connection between this optimization problem and a quadratic backward stochastic…
The method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is guided by intuition gained from the…
We establish fundamental connections between utility theories of wealth from the economic sciences and information-theoretic quantities. In particular, we introduce operational tasks based on betting where both gambler and bookmaker have…
In a previous paper, we introduced an axiomatic system for information thermodynamics, deriving an entropy function that includes both thermodynamic and information components. From this function we derived an entropic probability…