Displaying similar documents to “Mielnik's Probability Spaces and Characterization of Inner Product Spaces”

An extended problem to Bertrand's paradox

Mostafa K. Ardakani, Shaun S. Wulff (2014)

Discussiones Mathematicae Probability and Statistics

Similarity:

Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by...

Large losses-probability minimizing approach

Michał Baran (2004)

Applicationes Mathematicae

Similarity:

The probability minimizing problem for large losses of portfolio in discrete and continuous time models is studied. This gives a generalization of quantile hedging presented in [3].

Null events and stochastical independence

Giulianella Colleti, Romano Scozzafava (1998)

Kybernetika

Similarity:

In this paper we point out the lack of the classical definitions of stochastical independence (particularly with respect to events of 0 and 1 probability) and then we propose a definition that agrees with all the classical ones when the probabilities of the relevant events are both different from 0 and 1, but that is able to focus the actual stochastical independence also in these extreme cases. Therefore this definition avoids inconsistencies such as the possibility that an event A ...

Approximations of the ultimate ruin probability in the classical risk model using the Banach's fixed-point theorem and the continuity of the ruin probability

Jaime Martínez Sánchez, Fernando Baltazar-Larios (2022)

Kybernetika

Similarity:

In this paper, we show two applications of the Banach's Fixed-Point Theorem: first, to approximate the ultimate ruin probability in the classical risk model or Cramér-Lundberg model when claim sizes have some arbitrary continuous distribution and second, we propose an algorithm based in this theorem and some conditions to guarantee the continuity of the ruin probability with respect to the weak metric (Kantorovich). In risk theory literature, there is no methodology based in the Banach's...