On the Minkowski-H\"{o}lder type inequalities for generalized Sugeno integrals with an application

In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-H\"{o}lder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi in General Minkowski type and related inequalities for seminormed fuzzy integrals, Sahand Communications in Mathematical Analysis 1 (2014) 9--20 is not true. Next, we study the Minkowski-H\"{o}lder inequality for the lower Sugeno integral and the class of $\mu$-subadditive functions introduced in On Chebyshev type inequalities for generalized Sugeno integrals, Fuzzy Sets and Systems 244 (2014) 51--62. The results are applied to derive new metrics on the space of measurable functions in the setting of nonadditive measure theory. We also give a partial answer to the open problem 2.22 posed by Borzov\'a-Moln\'arov\'a and et al in The smallest semicopula-based universal integrals I: Properties and characterizations, Fuzzy Sets and Systems 271 (2015) 1--17.Comment: 19 page

On new immunization strategies under random shocks on the term structure of interest rates

We introduce new measures of immunization such as exponential duration referring, in particular, to Fong and Vasièek [7], Nawalkha and Chambers [14], Balbás and Ibánez [2], and Balbás et al. [3], but under the assumption of multiple shocks in the term structure of interest rates. These shocks are given by a random field. The cases of a single and multiple liabilities are discussed separately.portfolio, immunization, duration, term structure of interest rates, random field

On the Average Return Rate for a Group of Investment Funds

Supported by the KBN. Grant No. 11102B 018 14.In the paper a new definition of the average return rate for a group of investment (or pension) funds is proposed. The definition is derived via integration of the financial results of the group of funds during a given period of time. It satisfies a set of postulates which every coherent definition is supposed to fulfil contrary to the definition which is used in the Polish law of August 1997 on Organisation and Operation of Pension Funds. A very simple formula for the average return rate is available provided that the fund’s shares are stable in timeZadanie 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