A model of subjective supply-demand: the maximum Boltzmann/Shannon entropy solution (2008)
Piotrowski, Edward W., Sladkowski, Jan
We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique...
Inconsistency of the judgment matrix in the AHP method and the decision maker's knowledge (2008)
Szczypinska, Anna, Piotrowski, Edward W.
In this paper we propose a method for a quantitative estimation of the decision maker's knowledge in the context of the Analytic Hierarchy Process (AHP) in cases, where the judgment matrix is...
Deterministic definition of the capital risk (2008)
Szczypinska, Anna, Piotrowski, Edward W.
In this paper we propose a look at the capital risk problem inspired by deterministic, known from classical mechanics, problem of juggling. We propose capital equivalents to the Newton's laws of...
Piotrowski, Edward W., Schroeder, Malgorzata, Szczypinska, Anna
In this paper we compare two classical one-factor diffusion models which are used to model the term structure of interest rates. One of them is based on the Wiener-Bachelier process while the second...
Reinforcement learning in market games (2007)
Piotrowski, Edward W., Sladkowski, Jan, Szczypinska, Anna
Financial markets investors are involved in many games -- they must interact with other agents to achieve their goals. Among them are those directly connected with their activity on markets but one...
Projective Market Model Approach to AHP Decision-Making (2007)
Szczypinska, Anna, Piotrowski, Edward W.
In this paper we describe market in projective geometry language and give definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the...
The relativistic velocity addition law optimizes a forecast gambler's profit (2007)
Piotrowski, Edward W., Luczka, Jerzy
We extend the projective covariant bookmaker's bets model to the forecasting gamblers case. The probability of correctness of forecasts shifts probabilities of branching. The formula for the shift of...
Geometry of Financial Markets -- Towards Information Theory Model of Markets (2006)
Piotrowski, Edward W., Sladkowski, Jan
Most of parameters used to describe states and dynamics of financial market depend on proportions of the appropriate variables rather than on their actual values. Therefore, projective geometry seems...
The matrix rate of return (2006)
Zambrzycka, Anna, Piotrowski, Edward W.
In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes...
Kelly Criterion revisited: optimal bets (2006)
Piotrowski, Edward W., Schroeder, Malgorzata
Kelly criterion, that maximizes the expectation value of the logarithm of wealth for bookmaker bets, gives an advantage over different class of strategies. We use projective symmetries for a...
Quantum extension of European option pricing based on the Ornstein-Uhlenbeck process (2005)
Piotrowski, Edward W., Schroeder, Malgorzata, Zambrzycka, Anna
In this work we propose a option pricing model based on the Ornstein-Uhlenbeck process. It is a new look at the Black-Scholes formula which is based on the quantum game theory. We show the...
Makowski, Marcin, Piotrowski, Edward W.
We study a quantum version of the sequential game illustrating problems connected with making rational decisions. We compare the results that the two models (quantum and classical) yield. In the...
Universality of Measurements on Quantum Markets (2005)
Pakula, Ireneusz, Piotrowski, Edward W., Sladkowski, Jan
We reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. Two of the authors have recently proposed a quantum...
Quantum Games and Programmable Quantum Systems (2005)
Piotrowski, Edward W., Sladkowski, Jan
Attention to the very physical aspects of information characterizes the current research in quantum computation, quantum cryptography and quantum communication. In most of the cases quantum...
Piotrowski, Edward W., Sladkowski, Jan
We discuss some aspects of Astumian suggestions that combination of biased games (Parrondo's paradox) can explain performance of molecular motors. Unfortunately the model is flawed by explicit...
Cat's Dilemma - transitivity vs. intransitivity (2004)
Piotrowski, Edward W., Makowski, Marcin
We study a simple example of a sequential game illustrating problems connected with making rational decisions that are universal for social sciences. The set of chooser's optimal decisions that...
Quantum Game Theory in Finance (2004)
Piotrowski, Edward W., Sladkowski, J.
This is a short review of the background and recent development in quantum game theory and its possible application in economics and finance. The intersection of science and society is also...
Quantum computer: an appliance for playing market games (2003)
Piotrowski, Edward W., Sladkowski, Jan
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The authors have recently proposed a quantum description of...
Fixed point theorem for simple quantum strategies in quantum market games (2002)
A simple but nontrivial class of the quantum strategies in buying-selling games is presented. The player moves are a rational buying and an unconditional selling. The possibility of gaining extremal...
Quantization of Games: Towards Quantum Artificial Intelligence
Katarzyna Miakisz, Edward W. Piotrowski, Jan Sladkowski
On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. The idea of...
Quantum Auctions: Facts and Myths
Edward W. Piotrowski, Jan Sladkowski
Quantum game theory, whatever opinions may be held due to its abstract physical formalism, have already found various applications even outside the orthodox physics domain. In this paper we introduce...
Reinforcement Learning in Market Games
Edward W. Piotrowski, Jan Sladkowski, Anna Szczypinska
Financial markets investors are involved in many games - they must interact with other agents to achieve their goals. Among them are those directly connected with their activity on markets but one...
Kelly Criterion Revisited: Optimal Bets
Edward W. Piotrowski, Malgorzata Schroeder
Kelly criterion, that maximizes the expectation value of the logarithm of wealth for bookmaker bets, gives an advantage over different class of strategies. We use projective symmetries for a...
The relativistic velocity addition law optimizes a forecast gambler's profit
Edward W. Piotrowski, Jerzy Luczka
We extend the projective covariant bookmaker's bets model to the forecasting gamblers case. The probability of correctness of forecasts shifts probabilities of branching. The formula for the shift of...
Projective Market Model Approach to AHP Decision-Making
Anna Szczypinska, Edward W. Piotrowski
In this paper we describe market in projective geometry language and give definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the...
The relativistic velocity addition law optimizes a forecast gambler's profit
Edward W. Piotrowski, Jerzy Luczka
We extend the projective covariant bookmaker's bets model to the forecasting gamblers case. The probability of correctness of forecasts shifts probabilities of branching. The formula for the shift of...
Projective Market Model Approach to AHP Decision-Making
Anna Szczypinska, Edward W. Piotrowski
In this paper we describe market in projective geometry language and give definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the...
The Thermodynamics of Portfolios
Edward W. Piotrowski, Jan Sladkowski
We propose a new method of valuation of portfolios and their respective investing strategies. To this end we define a canonical ensemble of portfolios that allows to use the formalism of...
Edward W. Piotrowski, Jan Sladkowski
We propose a quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory. Quantum Zeno paradoxes and noncomutative quantum mecanics are...
What Was the Temperature of the Bagsik Financial Oscillator?
Edward W. Piotrowski, Jan Sladkowski
We argue that the recently published by Przystawa and Wolf model of the Bagsik financial oscillator is oversimplified and unrealistic. We propose and analyze a refined explanation of this rare...
Edward W. Piotrowski, Jan Sladkowski
We continue the analysis of quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory and quantum computing. The present paper is devoted...
Edward W. Piotrowski, Jan Sladkowski
We continue the analysis of quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory and quantum computing. The present paper is devoted...
Quantum-Like Approach to Financial Risk: Quantum Anthropic Principle
Edward W. Piotrowski, Jan Sladkowski
We continue the analysis of quantum-like description of market phenomena and economics. We show that it is possible to define a risk inclination operator acting in some Hilbert space that has a lot...
Trading by Quantum Rules - Quantum Anthropic Principle
Edward W. Piotrowski, Jan Sladkowski
This is a short review of the background and recent development in quantum game theory and its possible application in economics and finance. The intersection of science and society is discussed and...
Quantum solution to the Newcomb's paradox
Edward W. Piotrowski, Jan Sladkowski
We show that quantum game theory offers solution to the famous Newcomb's paradox (free will problem). Divine foreknowledge is not necessary for successful completion of the game because quantum...
Interference of quantum market strategies
Edward W. Piotrowski, Jan Sladkowski, Jacek Syska
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper is devoted to the analysis of interference of...
Quantum diffusion of prices and profits
Edward W. Piotrowski, Jan Sladkowski
We discuss the time evolution of quotation of stocks and commodities and show that quantum-like correction to the orthodox Bachelier model may be important. Our analysis shows that traders act as a...
Fixed point theorem for simple quantum strategies in quantum market games
A simple but nontrivial class of the quantum strategies in buying-selling games is presented. The player moves are a rational buying and an unconditional selling. The possibility of gaining extremal...
An Invitation to Quantum Game Theory
Edward W. Piotrowski, Jan Sladkowski
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent...
Quantum Computer: An Appliance for Playing Market Games
Edward W. Piotrowski, Jan Sladkowski
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The authors have recently proposed a quantum description of...
Arbitrage Risk Induced by Transaction Costs
Edward W. Piotrowski, Jan Sladkowski
We discuss the time evolution of quotation of stocks and commodities and show that they form an Ising chain. We show that transaction costs induce arbitrage risk that usually is neglected. The full...
The Next Stage: Quantum Game Theory
Edward W. Piotrowski, Jan Sladkowski
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent...
Quantum Game Theory in Finance
Edward W. Piotrowski, Jan Sladkowski
This is a short review of the background and recent development in quantum game theory and its possible application in economics and finance. The intersection of science and society is also...
Edward W. Piotrowski, Marcin Makowski
We study a simple example of a sequential game illustrating problems connected with making rational decisions that are universal for social sciences. The set of chooser's optimal decisions that...
Quantum Games and Programmable Quantum Systems
Edward W. Piotrowski, Jan Sladkowski
Attention to the very physical aspects of information characterizes the current research in quantum computation, quantum cryptography and quantum communication. In most of the cases quantum...
Universality of Measurements on Quantum Markets
Ireneusz Pakula, Edward W. Piotrowski, Jan Sladkowski
We reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. Two of the authors have recently proposed a quantum...
Kelly Criterion Revisited: Optimal Bets
Edward W. Piotrowski, Malgorzata Schroeder
Kelly criterion, that maximizes the expectation value of the logarithm of wealth for bookmaker bets, gives an advantage over different class of strategies. We use projective symmetries for a...
Anna Zambrzycka, Edward W. Piotrowski
In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes...
Geometry of Financial Markets - Towards Information Theory Model of Markets
Edward W. Piotrowski, Jan Sladkowski
Most of parameters used to describe states and dynamics of financial market depend on proportions of the appropriate variables rather than on their actual values. Therefore, projective geometry seems...
Quantum Cat's Dilemma: an Example of Intransitivity in a Quantum Game
Marcin Makowski, Edward W. Piotrowski
We study a quantum version of the sequential game illustrating problems connected with making rational decisions. We compare the results that the two models (quantum and classical) yield. In the...
Geometry of Financial Markets -- Towards Information Theory Model of Markets
Edward W. Piotrowski, Jan Sladkowski
Most of parameters used to describe states and dynamics of financial market depend on proportions of the appropriate variables rather than on their actual values. Therefore, projective geometry seems...
A model of subjective supply-demand: the maximum Boltzmann/Shannon entropy solution
Edward W. Piotrowski, Jan Sladkowski
We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique...
Inconsistency of the judgment matrix in the AHP method and the decision maker's knowledge
Anna Szczypinska, Edward W. Piotrowski
In this paper we propose a method for a quantitative estimation of the decision maker's knowledge in the context of the Analytic Hierarchy Process (AHP) in cases, where the judgment matrix is...
Kelly Criterion revisited: optimal bets
Edward W. Piotrowski, Malgorzata Schroeder
Kelly criterion, that maximizes the expectation value of the logarithm of wealth for bookmaker bets, gives an advantage over different class of strategies. We use projective symmetries for a...
Projective Market Model Approach to AHP Decision-Making
Anna Szczypinska, Edward W. Piotrowski
In this paper we describe market in projective geometry language and give definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the...
Reinforcement learning in market games
Edward W. Piotrowski, Jan Sladkowski, Anna Szczypinska
Financial markets investors are involved in many games -- they must interact with other agents to achieve their goals. Among them are those directly connected with their activity on markets but one...
Deterministic definition of the capital risk
Anna Szczypinska, Edward W. Piotrowski
In this paper we propose a look at the capital risk problem inspired by deterministic, known from classical mechanics, problem of juggling. We propose capital equivalents to the Newton's laws of...
Anna Zambrzycka, Edward W. Piotrowski
In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes...
Edward W. Piotrowski, Malgorzata Schroeder, Anna Szczypinska
In this paper we compare two classical one-factor diffusion models which are used to model the term structure of interest rates. One of them is based on the Wiener-Bachelier process while the second...