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1
Content available Stochastic analysis in the acoustics of damped sounds
Banek T.
Mechanics and Control
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2014
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Vol. 33, no. 1
1--4
EN
A stochastic model of sound propagation in damping medium is proposed. It consists of: (1) Ito's stochastic differential equation describing the sound propagation, (2) a potential which models the damping effects. However, due to presence of path integrals this model is elaborate and time consuming, hence inappropriate for numerical simulations and/or model calibrations. To make it simpler we used the classical results of stochastic analysis; Feynman-Kac formula and Girsanov tansformation obtaining easy-to-use computational procedure for practical purposes.
PL
W pracy przedstawiono stochastyczny model propagacji dźwięku w ośrodku tłumiącym. W badaniach, do modelowania propagacji dźwięku, zastosowano stochastyczne równanie różniczkowe Ito. Zjawiska tłumienia zamodełowano z zastosowaniem potencjału V(x). Ze względu na obecność całki po trajektoriach opracowanie modelu jest czasochłonne. W celu uproszczenia modelu i umożliwienia jego zastosowania w symulacjach numerycznych wykorzystano wyniki klasycznej analizy stochastycznej. Zastosowanie wzoru Feynmana--Kaca i transformacji Grisanova umożliwiło opracowanie łatwej w użyciu procedury obliczeniowej do zastosowań praktycznych.
2
Content available remote Incremental value of information for discrete-time partially observed stochastic systems
Banek T.
Control and Cybernetics
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2010
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Vol. 39, no 3
769-781
EN
A discrete-time stochastic control problem for general (nonlinear in state, control, observation and noise) models is considered. The same noise can enter into the state and into the observation equations, and the state/observation does not need to be affine with respect to the noise. Under mild assumptions the joint distribution function of the state/observation processes is obtained and used for computing the Gateaux and Frechet derivatives of the cost function. Under partial observation the control actions are restricted by the measurability requirement and we compute the Lagrange multiplier associated with this "information constraint". The multiplier is called a "dual", or "shadow" price, and in the literature of the subject is interpreted as an incremental value of information . The present and the future are two factors appearing in the multiplier and we study how they are balanced as time goes on. An algorithm for computing extremal controls in the spirit of R. Rishel (1985) is also obtained.
3
Content available remote Adaptive control of system entropy
Banek T., Kozłowski E.
Control and Cybernetics
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2006
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Vol. 35, no 2
279-289
EN
Controlling entropy of a system with unknown parameters is treated here as an adaptive control problem. Necessary conditions for optimality and an algorithm for computing extremal controls in the spirit of R. Rishel are obtained.
4
Active and passive learning in control processes application of the entropy concept
Banek T., Kozłowski E.
Systems Science
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2005
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Vol. 31, no 2
29-44
EN
The classical adaptive control and self-tuning problems are studied. They serve as models of active and passive learning processes. Comparison of optimal controls allows us to identify the "active" learning term in adaptive strategy. Next the entropy concept is applied to valuation of the learning processes.
5
Content available On an operational model of single investment selection with information cost
Banek T., Kozłowski E.
Control and Cybernetics
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2003
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Vol. 32, no 1
87-102
EN
An operational model of portfolio selection is presented. The target of a risk-neutral investor is to select the best portfolio composed of assets with the highest rate of return. The term "best" means that probability of attaining the return required by an investor is the largest for all possible stopping times, for which s/he has the right to buy information concerning the random vector of returns from investments (assets).
PL
Zaprezentowano pewien operatywny model wyboru portfela inwestycyjnego. Celem inwestora neutralnego względem ryzyka jest wybór najlepszego portfela złożonego z walorów o najwyższych stopach zwrotu. Pojęcie "najlepszy" oznacza, że prawdopodobieństwo osiągnięcia zwrotu wymaganego przez inwestora jest najwyższe dla wszystkich możliwych czasów stopu, przy których inwestor ma prawo zakupu informacji dotyczącej losowego wektora zwrotów z inwestycji (z walorów).
6
Content available remote Information pricing for portfolio optimization
Banek T., Kulikowski R.
Control and Cybernetics
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2003
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Vol. 32, no 4
867-882
EN
We consider the following problem: is there a rational or fair price for the reports made by analysts, experts, investor advisers concerning the rate of return (RR) of investments? We define the notion of the value of information included in the family of probability distributions of the RR. Next, we illustrate this notion for a linear-quadratic utility function.
7
Content available remote Value of Information for Portfolio Optimization
Banek T., Kulikowski R.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2003
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Vol. 51, nr 3
245-258
EN
We consider the following problem: is there a rational or fair price for the reports made by analysts, experts, investor advisers concerning the rate of return (RR) of investments? We define the notion of the value of information included in the family of probability distributions of the RR. Next, we illustrate this notion for a linear-quadratic utility function.
8
Content available remote Management of Intellectual Capital
Banek T., Kulikowski R.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2003
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Vol. 51, nr 3
205-211
EN
Two different types of firm's activity are considered as portfolio selection problems. First activity is an ordinary one. The second is innovative and extra-ordinary. To be profitable it must have enough of an "intellectual capital" (IC). Optimization problems for the firm are solved and the notion of IC is defind. Two different methodologies are discussed.
9
Content available remote Extension of the Portfolio Models with an Aspect of Purchase of Information
Banek T., Kozłowski E.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2003
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Vol. 51, nr 3
227-243
EN
An operational model of portfolio selection is presented in this paper. The model describes the situation of an investor who constructs a portfolio of assets according to the specific criterion and purchases information about the distribution of a random vector of returns from particular assets.
10
Content available remote Deratives of Diffusions with Applications in Finance
Banek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2003
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Vol. 51, nr 3
259-277
EN
Using the Isobe-Sato formula we identify deratives of the random variable [formula], where [formula] is a diffusion given by some SDE. It appears that the derative is propagated by a system of linear ODE's driven by some functionals of the sample [formula]. This leads to a new integral representation of the kernels of chaos expansion which is used for hedging of a given contingent claim by a self-financing portfolio.
11
Teoria konkurencji dystrybutorów energii
Banek T., Kaproń H., Rzymowski W.
Rynek Energii
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2000
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nr 1
2-7
PL
Przedstawiono teorię działania firm w warunkach konkurencji rynkowej. Pokazano, w jaki sposób wprowadzenie konkurencji do sektora energetycznego może wpłynąć na ceny zakupu i sprzedaży energii przez spółki dystrybucyjne. Sformułowane zależności matematyczne mogą być również wykorzystane, przy określonych założeniach, do opisu pozycji dystrybutora będącego monopolistą na rynku energii.
EN
Competition of companies is a typical feature of free market economy. True is also a contrary statement: lack of free market causes lack of competition, which means that free market and competition are mutually connected and that one does not exit without the other. The most importent criterion for evaluating activity of business is the level of profit. A firm, which achieves very little or none profit is rarely in position of great trust in financial institutions so very important while planning and carrying out a purpose concerning development. In the paper is presented a model showing dependence of achieving profit or energy distributors companies on: quantity of participation in a market, demand for energy, costs of distribution, flexibility of energy prices. Formula can be used for a description of individual electrical energy distributor position in a competition market.
12
Nowoczesne badania operacyjne - wyzwania i dylematy
Banek T.
Rynek Energii
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2000
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nr 2
26-31
13
Content available Numerical simulations of a portfolio selection model with information cost
Banek T., Kowalik P., Kozłowski E.
Control and Cybernetics
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2000
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Vol. 29, no 2
617-622
EN
Results of numerical simulations of a portfolio selection model with information cost are presented. Simulations are based on the real data from the Warsaw Stock Exchange. The results show that buying the information according to the presented model may lead to an essential reduction of investment risk depending on the required level of return. If the return level is not too high, reduction of risk really takes place.
14
Content available Portfolio selection model with information cost
Banek T., Kowalik P., Kozłowski E.
Control and Cybernetics
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1999
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Vol. 28, no 1
89-99
EN
A portfolio planning model which takes into account a cost of purchase of market information is considered. In the presented model, the objective of the investor is to maximize probability of attaining or exceeding the required return z. It is shown that the presented stochastic model reduces to a nonlinear programming problem that can be solved efficiently.
15
Content available remote Portfolio planning model with information costs.
Banek T., Kowalik P.
Badania Operacyjne i Decyzje
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1999
|
nr 2
5-14
EN
A portfolio planning model which assumes paying for market information essential for the investor is considered. More precisely, money spent on the information gives better estimates of the parameters of the random vector of returns, which yields reduction of the investment risk. On the other hand, more money spent on the purchase of the information means less money invested into assets. Therefore the goal of the investor is to find the trade-off between purchasing information and investing into assets themselves. This can be considered as an operational problem or, as is the case in this paper, as a planning problem. We also show how to reduce the planning model to a nonlinear programming problem that can be solved efficiently. Two numerical examples (with graphs showing geometry of the efficient set) are also given.
PL
W niniejszej pracy omówiono model decyzyjny wyboru portfela inwestycyjnego zakładający płacenie za istotną dla inwestora informację. Uściślając, pieniądze wydane na zakup informacji dają w zamian lepsze oszacowanie parametrów losowego wektora stóp zwrotu, co owocuje w postaci zredukowania ryzyka inwestycyjnego. Jednocześnie więcej pieniędzy wydanych na informacje oznacza mniej pieniędzy inwestowanych bezpośrednio w akcje. Dlatego też celem inwestora jest znalezienie optymalnego podziału kapitału na zakup informacji i inwestowanie w same akcje. Można to rozważać jako problem operacyjny, lub, jak w niniejszej pracy, jako problem planistyczny. W pracy pokazano także, jak zredukować model planistyczny do pewnego problemu programowania nieliniowego, który rozwiązano efektywnie. Podano również dwa przykłady numeryczne (z wykresami pokazującymi geometrię zbioru efektywnego).
16
Content available remote Parametric minimization of influence of stochastic didtribution in linear systems
Banek T.
Archives of Control Sciences
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1998
|
Vol. 7, no. 1/2
99-104
EN
A structure optimization problem in linear systems is considered. It is shown that parametric minimization (in the mean square sense) of influence of stochastic disturbation can be reduced to some nonlinear programming problem. Sufficient condition for equivalence of these problems and existence of their solutions are given. It is also shown how to apply the results to controlled systems.
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