Suppose that the process is observed sequentially. There are two random moments of time and , independent of X, and X is a Markov process given and . The transition probabilities of X change for the first time at time and for the second time at time . Our objective is to find a strategy which immediately detects the distribution changes with maximal probability based on observation of X. The corresponding problem of double optimal stopping is constructed. The optimal strategy is found...
The following problem in risk theory is considered. An insurance company, endowed with an initial capital a > 0, receives insurance premiums and pays out successive claims from two kind of risks. The losses occur according to a marked point process. At any time the company may broaden or narrow down the offer, which entails the change of the parameters of the underlying risk process. These changes concern the rate of income, the intensity of the renewal process and the distribution of claims....
The classical dowry, secretary, or beauty contest problem is extended. The author considers payoff functions that are more general than those of J. P. Gilbert and F. Mosteller [J. Amer. Statist. Assoc. 61 (1966), 35–73; MR0198637], A. G. Mucci [Ann. Statist. 1 (1973), 104–113; MR0383668] and Y. S. Chow, S. Moriguti, H. Robbins and S. M. Samuels [Israel J. Math. 2 (1964), 81–90; MR0176583].
A path through probability in honour of F. Thomas Bruss==================================The issue sponsored by
The following version of the two-player best choice problem is considered. Two players observe a sequence of i.i.d. random variables with a known continuous distribution. The random variables cannot be perfectly observed. Each time a random variable is sampled, the sampler is only informed whether it is greater than or less than some level specified by him. The aim of the players is to choose the best observation in the sequence (the maximal one). Each player can accept at most one realization of...
This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players' decisions. This is a form of equilibrium selection. Examples of correlated equilibria in nonzero-sum games related to the staff selection competition in the case of two departments...
The participation of mathematicians in the implementation of economic projects in Poland, in which mathematics-based methods played an important role, appeared sporadically in the past. Usually verified and known from the publications of published methods are adapted to solve related problems. The subject of the presentation will be the cooperation established by mathematicians and engineers in Wrocław in the second half of the twentieth century in the analysis of the effectiveness of engineering...
We consider a sequence of independent random variables with the known distribution observed sequentially. The observation n is a value of one order statistics s : n-th, where 1 ≤ s ≤ n. It the instances following the n-th observation it may remain of the s : m or it will be the value of the order statistics r : m (of m > n observations). Changing the rank of the observation, along with expanding a set of observations is a random phenomenon that is difficult to predict. From practical reasons...
In the 2016/17 academic year, for the second time, a poster design contest promoting the competition for "The best work in the theory of probability and applications of mathematics" was organized.
There is a number of popular books on mathematics and its connection with other human activities. The presented book “Games and Mathematics. Subtle Connections” belongs to this class but the author’s perspective is original (see [2] in references for links to other texts and reviews on the book ) by David Graham WellsThe title of the book is intriguing and outrageous at the same time. However, as it is possible to find in others’ opinion (see Thomas [1]), no one claims that mathematics is a...
XLIX Konkurs na najlepszą pracę studencką z teorii prawdopodobieństwa i zastosowań matematyki Konkurs organizowany jest przez Oddział Wrocławski PTM w celu propagowania wśród studentów problematyki teorii prawdopodobieństwa i zastosowań matematyki oraz promocji młodych matematyków uzyskujących oryginalne wyniki teoretyczne czy też rezultaty znajdujące zastosowania w innych dziedzinach nauki lub gospodarki. Prace zgłaszane na Konkurs są oceniane przez jury konkursu zgodnie z regulaminem konkursu...
Redakcja / Komitet Redakcyjny Redakcja Witold Kosiński (redaktor naczelny) wkos@pjwstk.edu.pl Mirosław Lachowicz (z-ca redaktora naczelnego) lachowic@mimuw.edu.pl Krzysztof Szajowski (z-ca redaktora naczelnego) Krzysztof.Szajowski@pwr.wroc.pl Komitet Redakcyjny Biologia matematyczna, biomatematyka Teoria gier i badania operacyjne Jacek Błażewicz, Wojciech Kordecki, Anna Jaśkiewicz, Krzysztof Szajowski, Mirosław Lachowicz, Ryszard Rudnicki Andrzej Wieczorek Matematyka finansowa i ubezpieczeniowa Statystyka...
we are pleased to present you with volume 45 Mathematica Applicanda. The contents of this volume are several articles with interesting examples of mathematical modeling in different issues and using different methods. This diversity is probably the result of the efforts of the entire editorial team and to some extent reflects our research interests. Signals in the form of articles from outside Poland are extremely valuable. The fact that the portal of the magazine is visited by Internet users from...
Mathematica Applicanda is very pleased to present Volume 44(1). This volume focuses on a special topic in Probability Theory, namely on the Theory and Applications of Optimal Stopping. The journal Mathematica Applicanda is for several reasons a natural place for this subject. Our longtime editor Prof. Bartoszyński was much interested in problems of Optimal Stopping and helped to make such problems known among distinguished Polish mathematicians. And, as many publications clearly indicate, this...
The information about the Editorial Board of the chapter.
This book presents a careful and comprehensive introduction to some of the most important mathematical topics required for a thorough understanding of financial markets and the quantitative methods used to manage the assets there. The author has focused on arbitrage theory for pricing contingent claims and statistical models and methods to analyze data from financial markets. It is quit new idea to combine the data analysis methods for mathematical models of founds, options and other derivatives....
Guest Editor of the Special Chapter
Scientific activity can be described by specifying a different set of features. For so characterized the activity we can use one of the statistical methods that allow for aggregation and classification. Experts in the subject know that aggregation can be performed in different ways and at different levels of generated classes finish. In this note I'll try to mention the reasons which may give rise to separate distinct group of research in the discipline of applied mathematics or applications of...
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