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Limit state analysis on the un-repeated multiple selection bounded confidence model

Jiangbo Zhang, Yiyi Zhao (2023)

Kybernetika

In this paper, we study the opinion evolution over social networks with a bounded confidence rule. Node initial opinions are independently and identically distributed. At each time step, each node reviews the average opinions of several different randomly selected agents and updates its opinion only when the difference between its opinion and the average is below a threshold. First of all, we provide probability bounds of the opinion convergence and the opinion consensus, are both nontrivial events...

Limiting distribution for a simple model of order book dynamics

Łukasz Kruk (2012)

Open Mathematics

A continuous-time model for the limit order book dynamics is considered. The set of outstanding limit orders is modeled as a pair of random counting measures and the limiting distribution of this pair of measure-valued processes is obtained under suitable conditions on the model parameters. The limiting behavior of the bid-ask spread and the midpoint of the bid-ask interval are also characterized.

Limits of Bayesian decision related quantities of binomial asset price models

Wolfgang Stummer, Wei Lao (2012)

Kybernetika

We study Bayesian decision making based on observations X n , t : t { 0 , T n , 2 T n , ... , n T n } ( T > 0 , n ) of the discrete-time price dynamics of a financial asset, when the hypothesis a special n -period binomial model and the alternative is a different n -period binomial model. As the observation gaps tend to zero (i. e. n ), we obtain the limits of the corresponding Bayes risk as well as of the related Hellinger integrals and power divergences. Furthermore, we also give an example for the “non-commutativity” between Bayesian statistical and...

L'implication statistique entre variables modales

Marc Bailleul, Régis Gras (1994)

Mathématiques et Sciences Humaines

L'implication statistique, selon R.Gras, permet d'associer à un ensemble de variables binaires ou fréquentielles un préordre représentable par un graphe non symétrique et par une hiérarchie ascendante. L'analyse d'un questionnaire à modalités totalement ordonnées nous contraint, pour conserver l'information maximale, à étendre cette notion à des variables modales et, par suite et a fortiori, à des variables ordinales qui s'y ramènent. A la suite de cette construction, on examine les contributions...

Linear complementarity problems and bi-linear games

Gokulraj Sengodan, Chandrashekaran Arumugasamy (2020)

Applications of Mathematics

In this paper, we define bi-linear games as a generalization of the bimatrix games. In particular, we generalize concepts like the value and equilibrium of a bimatrix game to the general linear transformations defined on a finite dimensional space. For a special type of 𝐙 -transformation we observe relationship between the values of the linear and bi-linear games. Using this relationship, we prove some known classical results in the theory of linear complementarity problems for this type of 𝐙 -transformations....

Linear-quadratic differential games: from finite to infinite dimension

Michel C. Delfour (2008)

Applicationes Mathematicae

The object of this paper is the generalization of the pioneering work of P. Bernhard [J. Optim. Theory Appl. 27 (1979)] on two-person zero-sum games with a quadratic utility function and linear dynamics. It relaxes the semidefinite positivity assumption on the matrices in front of the state in the utility function and introduces affine feedback strategies that are not necessarily L²-integrable in time. It provides a broad conceptual review of recent results in the finite-dimensional case for which...

Local stability and differentiability of the Mean–Conditional Value at Risk model defined on the mixed–integer loss functions

Martin Branda (2010)

Kybernetika

In this paper, we study local stability of the mean-risk model with Conditional Value at Risk measure where the mixed-integer value function appears as a loss variable. This model has been recently introduced and studied in~Schulz and Tiedemann [16]. First, we generalize the qualitative results for the case with random technology matrix. We employ the contamination techniques to quantify a possible effect of changes in the underlying probability distribution on the optimal value. We use the generalized...

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