In this paper, we propose a new generalization of the classical discrete Choquet integral to the ... more In this paper, we propose a new generalization of the classical discrete Choquet integral to the multivalued framework in terms of an admissible order that refines the natural partial order on the considered value set. The new Choquet-like operator takes as input a finite number of values of a given type, in particular real numbers, intervals, and vectors, and returns a single output value of the same type as the input values. We give necessary and sufficient conditions for the operator to be monotone with respect to the admissible order. We then provide a complete characterization of the Choquet-like operator as an aggregation function with respect to the admissible order and study its selected special cases.
In this paper we consider asmissible and minimax estimation of the parameter ~r in the gamma dist... more In this paper we consider asmissible and minimax estimation of the parameter ~r in the gamma distribution with truncated parameter space. We give a necessary and sufficient condition for minimaxity (Theorem 1) and obtain the classes of new minimax and asmissible estimators. The results of the paper can be applied to estimation of parameters in the normal, lognormal, Pareto, generalized gamma, generalized Laplace and other distributions.
In the 1970s Kahneman and Tversky conducted a series of experiments which suggested that people d... more In the 1970s Kahneman and Tversky conducted a series of experiments which suggested that people do not behave accordingly to the von Neumann-Morgenstern’s Expected Utility Theory. Therefore, they proposed an alternative theory, called the Cumulative Prospect Theory, in which they used the Choquet integral with respect to distorted probability measures to describe decision making in risk and uncertainty conditions. The paper presents the generalized Arrow-Pratt risk aversion model, when the classic expected value is replaced by the generalized Choquet integral. To do this, we require necessary and sufficient conditions for the Jensen type inequality for the generalized Choquet integral with respect to arbitrary monotone measure, that is not an additive set function. We will provide some results of this type and point the difficulties that show up without the additivity assumption.
In the paper, we characterize the class of all pairs of fuzzy implications and dual fuzzy implica... more In the paper, we characterize the class of all pairs of fuzzy implications and dual fuzzy implications such that the q-integral and q-cointegral coincide. This gives a solution to the problem posed by Didier Dubois during the conference FSTA 2016, the 13th International Conference on Fuzzy Set Theory and Applications. As a corollary, we obtain the necessary and sufficient conditions under which the seminormed fuzzy integral and the semiconormed fuzzy integral are equal for all measurable functions.
Abstract In this paper we define a novel survival function motivated by real life problems, which... more Abstract In this paper we define a novel survival function motivated by real life problems, which generalizes the super level measure introduced by Do and Thiele (2015). This concept is based on conditional aggregation operators extending the definition of aggregation operators introduced by Calvo et al (2002) for all bounded measurable functions and not only for finite sequences. Some basic properties and several examples of conditional aggregation operators are presented. Using the novel survival function, the Choquet-Stieltjes functional is introduced and the conditions are indicated under which this functional can be called an integral. The new functional generalizes several known integrals including the Choquet-Stieltjes integral as well as Choquet integral with respect to level dependent capacity introduced by Greco et al (2011).
Extending the concept of level measure µ({f a}) we introduce a generalized level measure based on... more Extending the concept of level measure µ({f a}) we introduce a generalized level measure based on a family of conditional aggregations operators. We investigate in detail several basic properties, including connections with the family of level measures, the generalized survival function and the transformation of monotone measures to hyperset. Applications in scientometrics and information science are described.
In this paper, we discuss selected aspects of the problem of assets/liabilities portfolio immuniz... more In this paper, we discuss selected aspects of the problem of assets/liabilities portfolio immunization against changes in the interest rate structure. This issue is important for a number of financial institutions: banks, insurance companies, investment funds or pension funds. We give some new estimates for the value of the portfolio at a fixed time in the future and discuss their relationship with the existing results.
Abstract In this paper we provide a full characterization of functions G : [ 0 , y ¯ ] 2 → [ 0 , ... more Abstract In this paper we provide a full characterization of functions G : [ 0 , y ¯ ] 2 → [ 0 , y ¯ ] satisfying the distributivity equation G ( a ∘ b , a ∘ c ) = a ∘ G ( b , c ) for any a , b , c with a fixed binary operation ∘ : [ 0 , y ¯ ] 2 → [ 0 , y ¯ ] generalizing minimum and maximum and y ¯ ∈ ( 0 , ∞ ] . The above functional equation with an admissible function G and ∘ being minimum [resp. maximum] has appeared when studying properties of minitive [resp. maxitive] homogeneity for the recently introduced upper n-Sugeno integral.
On donne une condition necessaire et suffisante pour la minimaxite et on obtient les classes de n... more On donne une condition necessaire et suffisante pour la minimaxite et on obtient les classes de nouveaux estimateurs minimax et admissibles
This paper deals with new immunization strategies for a noncallable and default-free bond portfol... more This paper deals with new immunization strategies for a noncallable and default-free bond portfolio. This approach refers to the Fong and Vasicek (1984), the Nawalkha and Chambers (1996), the Balbàs and Ibáňez (1998), and the Balbàs, Ibáňez and Lopez (2002) studies among others and relies on minimizing a single-risk measure which is a linear combination of the duration gap and the dispersion of portfolio payments.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukęZadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej nauk
Extending the concept of level measure µ({f a}) we introduce a generalized level measure based on... more Extending the concept of level measure µ({f a}) we introduce a generalized level measure based on a family of conditional aggregations operators. We investigate in detail several basic properties, including connections with the family of level measures, the generalized survival function and the transformation of monotone measures to hyperset. Applications in scientometrics and information science are described.
Jedną z najwazniejszych z praktycznego punktu widzenia wlasności skladek ubezpieczeniowych jest i... more Jedną z najwazniejszych z praktycznego punktu widzenia wlasności skladek ubezpieczeniowych jest iteracyjnośc. Pojecie iteracyjności zostalo wprowadzone w latach 70. ubieglego stulecia i od tej pory wielu matematykow i ekonomistow badalo te wlasnośc dla roznych funkcjonalow zdefiniowanych w matematyce finansowej i ubezpieczeniowej. W niniejszej pracy omawiamy iteracyjnośc skladek zerowej uzyteczności oraz mean-value zdefiniowanych w ujeciu dwoch roznych teorii ekonomicznych. Pierwsza z nich, teoria skumulowanej perspektywy Kahnemana-Tversky’ego, zaklada, ze przy podejmowaniu decyzji w warunkach ryzyka i niepewności ludzie znieksztalcają prawdopodobienstwa zyskow i strat oraz uzywają funkcji wartości do oceny wielkości zmian w posiadanym majątku. W drugim z modeli, uwzgledniającym zalozenia teorii nieokreśloności, przyjmujemy, ze nie mamy calkowitej wiedzy na temat rozkladu szkody. Przeprowadzona w tym artykule analiza pozwoli nam wzbogacic informacje, jakie posiadamy na temat iteracy...
The aim of this paper is to examine arbitrage free models and investigate which of them imply wel... more The aim of this paper is to examine arbitrage free models and investigate which of them imply well known and widely applied classical duration strategy. Problem of a noncallable and default-free bond portfolio immunization is studied in a 3-period model of time with a fixed investment strategy either under known optimization criterions such as maxmin, Bayesian, Gamma-maxmin, Markowitz-type and others. In some models there are anomalies since, it is proved that, any strategy is optimal. A notable fact is that the Markowitz approach is free from such anomalies and, moreover, in some cases occurs to be a duration strategy.
In this paper, we propose a new generalization of the classical discrete Choquet integral to the ... more In this paper, we propose a new generalization of the classical discrete Choquet integral to the multivalued framework in terms of an admissible order that refines the natural partial order on the considered value set. The new Choquet-like operator takes as input a finite number of values of a given type, in particular real numbers, intervals, and vectors, and returns a single output value of the same type as the input values. We give necessary and sufficient conditions for the operator to be monotone with respect to the admissible order. We then provide a complete characterization of the Choquet-like operator as an aggregation function with respect to the admissible order and study its selected special cases.
In this paper we consider asmissible and minimax estimation of the parameter ~r in the gamma dist... more In this paper we consider asmissible and minimax estimation of the parameter ~r in the gamma distribution with truncated parameter space. We give a necessary and sufficient condition for minimaxity (Theorem 1) and obtain the classes of new minimax and asmissible estimators. The results of the paper can be applied to estimation of parameters in the normal, lognormal, Pareto, generalized gamma, generalized Laplace and other distributions.
In the 1970s Kahneman and Tversky conducted a series of experiments which suggested that people d... more In the 1970s Kahneman and Tversky conducted a series of experiments which suggested that people do not behave accordingly to the von Neumann-Morgenstern’s Expected Utility Theory. Therefore, they proposed an alternative theory, called the Cumulative Prospect Theory, in which they used the Choquet integral with respect to distorted probability measures to describe decision making in risk and uncertainty conditions. The paper presents the generalized Arrow-Pratt risk aversion model, when the classic expected value is replaced by the generalized Choquet integral. To do this, we require necessary and sufficient conditions for the Jensen type inequality for the generalized Choquet integral with respect to arbitrary monotone measure, that is not an additive set function. We will provide some results of this type and point the difficulties that show up without the additivity assumption.
In the paper, we characterize the class of all pairs of fuzzy implications and dual fuzzy implica... more In the paper, we characterize the class of all pairs of fuzzy implications and dual fuzzy implications such that the q-integral and q-cointegral coincide. This gives a solution to the problem posed by Didier Dubois during the conference FSTA 2016, the 13th International Conference on Fuzzy Set Theory and Applications. As a corollary, we obtain the necessary and sufficient conditions under which the seminormed fuzzy integral and the semiconormed fuzzy integral are equal for all measurable functions.
Abstract In this paper we define a novel survival function motivated by real life problems, which... more Abstract In this paper we define a novel survival function motivated by real life problems, which generalizes the super level measure introduced by Do and Thiele (2015). This concept is based on conditional aggregation operators extending the definition of aggregation operators introduced by Calvo et al (2002) for all bounded measurable functions and not only for finite sequences. Some basic properties and several examples of conditional aggregation operators are presented. Using the novel survival function, the Choquet-Stieltjes functional is introduced and the conditions are indicated under which this functional can be called an integral. The new functional generalizes several known integrals including the Choquet-Stieltjes integral as well as Choquet integral with respect to level dependent capacity introduced by Greco et al (2011).
Extending the concept of level measure µ({f a}) we introduce a generalized level measure based on... more Extending the concept of level measure µ({f a}) we introduce a generalized level measure based on a family of conditional aggregations operators. We investigate in detail several basic properties, including connections with the family of level measures, the generalized survival function and the transformation of monotone measures to hyperset. Applications in scientometrics and information science are described.
In this paper, we discuss selected aspects of the problem of assets/liabilities portfolio immuniz... more In this paper, we discuss selected aspects of the problem of assets/liabilities portfolio immunization against changes in the interest rate structure. This issue is important for a number of financial institutions: banks, insurance companies, investment funds or pension funds. We give some new estimates for the value of the portfolio at a fixed time in the future and discuss their relationship with the existing results.
Abstract In this paper we provide a full characterization of functions G : [ 0 , y ¯ ] 2 → [ 0 , ... more Abstract In this paper we provide a full characterization of functions G : [ 0 , y ¯ ] 2 → [ 0 , y ¯ ] satisfying the distributivity equation G ( a ∘ b , a ∘ c ) = a ∘ G ( b , c ) for any a , b , c with a fixed binary operation ∘ : [ 0 , y ¯ ] 2 → [ 0 , y ¯ ] generalizing minimum and maximum and y ¯ ∈ ( 0 , ∞ ] . The above functional equation with an admissible function G and ∘ being minimum [resp. maximum] has appeared when studying properties of minitive [resp. maxitive] homogeneity for the recently introduced upper n-Sugeno integral.
On donne une condition necessaire et suffisante pour la minimaxite et on obtient les classes de n... more On donne une condition necessaire et suffisante pour la minimaxite et on obtient les classes de nouveaux estimateurs minimax et admissibles
This paper deals with new immunization strategies for a noncallable and default-free bond portfol... more This paper deals with new immunization strategies for a noncallable and default-free bond portfolio. This approach refers to the Fong and Vasicek (1984), the Nawalkha and Chambers (1996), the Balbàs and Ibáňez (1998), and the Balbàs, Ibáňez and Lopez (2002) studies among others and relies on minimizing a single-risk measure which is a linear combination of the duration gap and the dispersion of portfolio payments.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukęZadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej nauk
Extending the concept of level measure µ({f a}) we introduce a generalized level measure based on... more Extending the concept of level measure µ({f a}) we introduce a generalized level measure based on a family of conditional aggregations operators. We investigate in detail several basic properties, including connections with the family of level measures, the generalized survival function and the transformation of monotone measures to hyperset. Applications in scientometrics and information science are described.
Jedną z najwazniejszych z praktycznego punktu widzenia wlasności skladek ubezpieczeniowych jest i... more Jedną z najwazniejszych z praktycznego punktu widzenia wlasności skladek ubezpieczeniowych jest iteracyjnośc. Pojecie iteracyjności zostalo wprowadzone w latach 70. ubieglego stulecia i od tej pory wielu matematykow i ekonomistow badalo te wlasnośc dla roznych funkcjonalow zdefiniowanych w matematyce finansowej i ubezpieczeniowej. W niniejszej pracy omawiamy iteracyjnośc skladek zerowej uzyteczności oraz mean-value zdefiniowanych w ujeciu dwoch roznych teorii ekonomicznych. Pierwsza z nich, teoria skumulowanej perspektywy Kahnemana-Tversky’ego, zaklada, ze przy podejmowaniu decyzji w warunkach ryzyka i niepewności ludzie znieksztalcają prawdopodobienstwa zyskow i strat oraz uzywają funkcji wartości do oceny wielkości zmian w posiadanym majątku. W drugim z modeli, uwzgledniającym zalozenia teorii nieokreśloności, przyjmujemy, ze nie mamy calkowitej wiedzy na temat rozkladu szkody. Przeprowadzona w tym artykule analiza pozwoli nam wzbogacic informacje, jakie posiadamy na temat iteracy...
The aim of this paper is to examine arbitrage free models and investigate which of them imply wel... more The aim of this paper is to examine arbitrage free models and investigate which of them imply well known and widely applied classical duration strategy. Problem of a noncallable and default-free bond portfolio immunization is studied in a 3-period model of time with a fixed investment strategy either under known optimization criterions such as maxmin, Bayesian, Gamma-maxmin, Markowitz-type and others. In some models there are anomalies since, it is proved that, any strategy is optimal. A notable fact is that the Markowitz approach is free from such anomalies and, moreover, in some cases occurs to be a duration strategy.
Uploads
Papers by Marek Kałuszka