### Mean-variance optimal local reinsurance contracts

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Convex records in Euclidean space are considered. We provide both lower and upper bounds on the probability ${p}_{n}\left(k\right)$ that in a sequence of random vectors ${X}_{1}$,..., ${X}_{n}$ there are exactly k records.

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.

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.

In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-Hölder 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 [11] is not true. Next, we study the Minkowski-Hölder inequality for the lower Sugeno integral and the...

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...

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...

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