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On a unified approach to the Cramer-Rao type inequalities

100%
Kałuszka M.
Mathematica Applicanda
|
1985
|
tom 16
|
nr 30
PL
.
EN
The aim of this paper is to give a unified approach to Cramer-Rao type inequalities for risk and Bayes risk functions under squared error loss. In the paper, the results connected with an arbitrary convex loss are also presented.
2
Content available remote

Estimates of some probabilities in multidimensional convex records

100%
Kałuszka M.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 1
1-11
EN
Convex records in Euclidean space are considered. We provide both lower and upper bounds on the probability $p_n(k)$ that in a sequence of random vectors $X_1$,..., $X_n$ there are exactly k records.
3
Content available remote

A note on order statistics from symmetrically distributed samples

64%
Kałuszka M., Okolewski A.
Applicationes Mathematicae
|
2011
|
tom 38
|
nr 4
477-483
EN
We present a first moment distribution-free bound on expected values of L-statistics as well as properties of some numerical characteristics of order statistics, in the case when the observations are possibly dependent symmetrically distributed about the common mean. An actuarial interpretation of the presented bound is indicated.
4
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Generalized duration measures in a risk immunization setting. Implementation of the Heath-Jarrow-Morton model

64%
Kondratiuk-Janyska A., Kałuszka M.
Applicationes Mathematicae
|
2006
|
tom 33
|
nr 2
145-157
EN
The aim of this paper is to set different lower bounds on the change of the expected net cash flow value at time H > 0 in general term structure models, referring to the studies of Fong and Vasiček (1984), Nawalkha and Chambers (1996), and Balbás and Ibáñez (1998) among others. New immunization strategies are derived with new risk measures: generalized duration and generalized M-absolute of Nawalkha and Chambers, and exponential risk measure. Furthermore, examples of specific one-factor HJM models are provided and the problem of immunization is discussed.
5
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On risk minimizing strategies for default-free bond portfolio immunization

64%
Kałuszka M., Kondratiuk-Janyska A.
Applicationes Mathematicae
|
2004
|
tom 31
|
nr 3
259-272
EN
This paper presents new strategies for bond portfolio immunization which combine the time-honored duration with the M-Absolute measure defined by Nawalkha and Chambers (1996). The innovation consists in considering an average shock in a fixed time period as a random variable with mean μ or, alternatively, with normal distribution with mean μ and variance σ². Additionally, an extension to arbitrage free models of polynomial shocks is provided. Moreover, the Fisher and Weil model, the M-Absolute strategy and a new one are compared empirically with respect to financial liquidity.
6
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Assets/liabilities portfolio immunization as an optimization problem

45%
Kondratiuk-Janyska A., Kałuszka M.
Control and Cybernetics
|
2006
|
tom 35
|
nr 2
335-349
7
Content available remote

Mean-variance optimal local reinsurance contracts

32%
Kałuszka M.
Control and Cybernetics
|
2003
|
tom 32
|
nr 4
883-896
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