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1

Mariana Smoluchowskiego ujęcie zasady przyczynowości w badaniach ruchów Browna

100%

Roskal Z. E.

Zagadnienia Filozoficzne w Nauce

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2017

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issue 62

99-126

PL

Marian Smoluchowski solved the greatest scientific problem of his time. It was the explanation of the phenomenon of the Brownian motion. In the article, I show that Smoluchowski in fact in this explanation used an ontological interpretation of the causality principle, although in his writings he applied it also in the epistemological interpretation. This is understandable because in the scientific practice some kinds of ontological commitment are required.

2

Marian Smoluchowski’s Contributions to the Philosophy of Causation

88%

Roskal Z.

Organon

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2018

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vol. 50

5-18

EN

Marian Smoluchowski was a prominent Polish physicist whose greatest achievement was the development – independently of Albert Einstein – of the mathematical theory of Brownian motion. In his theoretical view of the problem of Brownian motion Smoluchowski employed the concept of causal relevance, which was never analysed in numerous publications devoted to his scientific achievement. In this article I am attempting to demonstrate that the concept of causal relevance which Smoluchowski employed in his works devoted to the issue of Brownian motion may be interpreted as analogous to the concept of causal relevance articulated by Max Kistler. I present a number of arguments which demonstrate that just such a concept of causal relevance was established by Smoluchowski. Since the explanation of the phenomenon of Brownian motion presented by Smoluchowski has been universally accepted, so in the same way the physicalistic concept of causal relevance has been widely propagated. In this I detect Smoluchowski’s contribution to the philosophy of causality.

3

Fluktuujący świat Mariana Smoluchowskiego

75%

Fuliński A.

Zagadnienia Filozoficzne w Nauce

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2017

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issue 62

127-138

PL

The main goal of this paper is to present the Marian Smoluchowski’s work on thermal and primordial fluctuations which are the main cause of Brownian motion and one of the first empirical evidences for molecular structure of matter.

4

O pewnych kryteriach inwestowania w opcje na akcje

75%

Warowny T.

Metody Ilościowe w Badaniach Ekonomicznych

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2012

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vol. 13

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issue 3

243-252

PL

W artykule scharakteryzowano opcje na akcje. Wyjaśniono podstawowe pojęcia, takie jak: termin wykonania, termin wygaśnięcia, cena wykonania, cena opcji. Do opisu ewolucji cen akcji wykorzystano geometryczny ruch Browna. Sformułowano kilka problemów dotyczących inwestowania w opcje na akcje otrzymując zadania programowania stochastycznego. Korzystając z własności ruchu Browna pokazano, w jaki sposób szacować prawdopodobieństwa zdarzeń polegających na osiągnięciu przez inwestora zysków na żądanym poziomie lub przy ustalonym poziomie ryzyka. Dla każdego z zadań dokonano przykładowych obliczeń.

EN

This article describes the stock options. It explains the basic concepts, such as settlement date, expiration date, strike price and premium. To describe the evolution of share prices we used the geometrical Brownian motionWe presented the several criteria for investment in options and shares and then obtained the exercises of stochastic programming. Using the properties of Brownian motion, we explained how to estimate the probability of achieving the profit of desired amount or on fixed level of risk. For each of these criteria we presented the sample calculations.

5

Insurance drawdown-type contracts for a phase-type risk process perturbed by Brownian motion

75%

Palmowski Z., Tumilewicz J.

Śląski Przegląd Statystyczny

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2017

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issue 15 (21)

201-226

EN

In this paper we consider the insurance polices based on drawdown and drawup events where an underlying asset is derived by a classical risk process with phasetype claim sizes perturbed by Brownian motion. The drawdown/drawup process we define as a difference between the historical maximum/minimum and current asset value. We consider four contracts presented in [Palmowski, Tumilewicz 2016]. The first one is an insurance contract where the protection buyer is paying a constant premium with intensity p until the drawdown of fixed size occurs. In return he/she receives a certain insured amount at the drawdown epoch. The second insurance contract may expire early if a certain fixed drawup event occurs prior to a fixed drawdown. The last two contracts are extensions of the previous ones by an additional cancellable feature which allows an investor to terminate the contract earlier. We focus here on an extensive numerical analysis when claim sizes are phase-type.

6

Estymacja wariancji arytmetycznego ruchu Browna na podstawie znanych wartości minimum, maksimum, końcowej oraz dryfu

75%

Perczak G., Fiszeder P.

Przegląd Statystyczny

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2013

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vol. 60

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issue 1

39-62

PL

W opracowaniu poruszony jest problem wyznaczenia wariancji stopy zwrotu instrumentu finansowego na podstawie rynkowych notowań dziennych cen otwarcia, minimalnej, maksymalnej i zamknięcia. Wykorzystując znajomość łącznego rozkładu minimum, maksimum i wartości końcowej arytmetycznego ruchu Browna dokonano analizy porównawczej znanych estymatorów wariancji. Wyznaczono formuły wartości oczekiwanych bardzo wielu funkcji zmiennych losowych, które posłużyły do konstrukcji tych estymatorów. Ponadto, na ich podstawie zaproponowano nowy estymator wariancji. Dokonano analizy założeń, które przyjęto przy konstrukcji tego estymatora. Metodami analitycznymi porównano jego efektywność z efektywnością podstawowych znanych estymatorów zmienności dziennej.

EN

This paper examines the problem of calculating the variance of returns of a financial instrument which is based upon the historical opening, closing, high, and low prices. For this purpose, the knowledge of the joint distribution of minimum, maximum and final values of arithmetic Brownian motion was used. It gave a possibility to make a comparative analysis of the variance estimators. The formulae of expected values of many random variables, which were used for the construction of these estimators were calculated. Moreover, on the basis of those formulae, the new estimator of variance was proposed. The assumptions that were adopted for the construction of the estimator were examined. The efficiency of the proposed estimator was compared with the efficiency of the well-known estimators of daily volatility.

7

Słabe łamanie ergodyczności vs. determinizm

75%

Fuliński A.

Zagadnienia Filozoficzne w Nauce

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2015

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issue 59

83-100

PL

All physical processes are deterministic de iure. Physicists speak about different types of determinism of physical processes, depending on the degree with which their course can be anticipated. Usually, the course of ergodic processes can be predicted with less certainty than the non-ergodic ones, the latter being integrable. Recent measurements of motions of single particles in composite systems, especially in living biological cells, show that such motions are, in most cases, breaking the Boltzmann’s ergodic hypothesis. On the other hand, their trajectories are random, i.e., one cannot know a priori where the particle will be even in near future. This leads to conclusion that many existing in nature processes are nonergodic but not integrable, therefore predictable only in the mean, representing still other type of determinism.

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3 Zagadnienia Filozoficzne w Nauce

1 Metody Ilościowe w Badaniach Ekonomicznych

1 Organon

1 Przegląd Statystyczny

1 Śląski Przegląd Statystyczny

2 Fuliński A.

1 Fiszeder P.

1 Palmowski Z.

1 Perczak G.

1 Roskal Z.

1 Roskal Z. E.

1 Tumilewicz J.

1 Warowny T.

1 2018

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Mariana Smoluchowskiego ujęcie zasady przyczynowości w badaniach ruchów Browna

Marian Smoluchowski’s Contributions to the Philosophy of Causation

Fluktuujący świat Mariana Smoluchowskiego

O pewnych kryteriach inwestowania w opcje na akcje

Insurance drawdown-type contracts for a phase-type risk process perturbed by Brownian motion

Estymacja wariancji arytmetycznego ruchu Browna na podstawie znanych wartości minimum, maksimum, końcowej oraz dryfu

Słabe łamanie ergodyczności vs. determinizm