We describe a new model of multiple reinsurance. The main idea is that the reinsurance premium is paid conditionally. It is motivated by some analysis of the ultimate price of the reinsurance contract. For simplicity we assume that the underlying risk pricing functional is the L₂-norm. An unexpected relation to the general theory of sample regularity of stochastic processes is given.

In this paper we present and develop, only elementarily, an axiomatic frame for some special fuzzy relations, the so called relational probabilities, which happen to be families of functions which in some cases are quantic probabilities [1] on sublattices of a given lattice; in this way we obtain calculations similar to the ordinary ones but based on a weaker lattice background. This framework is inspired on the presentation of conditional probability on Boolean algebras made in [5] and in [4] and...

Relations for the marginal, joint, conditional characteristic functions of k-th upper and lower record values from generalized Pareto distribution and inverse generalized Pareto distribution are given.

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.We discuss weak limit theorems for a uniformly negligible triangular array (u.n.t.a.) in Z = [0, ∞) × [0, ∞)^d as well as for the associated with it sum and extremal processes on an open subset S . The complement of S turns out to be the explosion area of the limit Poisson point process. In order to prove our criterion for weak convergence of the sum processes we introduce and study sum processes over explosion area....

Let $C[0,t]$ denote a generalized Wiener space, the space of real-valued continuous functions on the interval $[0,t]$, and define a random vector $Z_n:C[0,t]\to {ℝ}^{n+1}$ by $$Z_n\left(x\right)=\left(x\left(0\right)+a\left(0\right),{\int }_0^{t_1}h\left(s\right)\mathrm{d}x\left(s\right)+x\left(0\right)+a\left(t_1\right),\cdots ,{\int }_0^{t_n}h\left(s\right)\mathrm{d}x\left(s\right)+x\left(0\right)+a\left(t_n\right)\right),$$ where $a\in C[0,t]$, $h\in L_2[0,t]$, and $0<t_1<\cdots <t_n\le t$ is a partition of $[0,t]$. Using simple formulas for generalized conditional Wiener integrals, given $Z_n$ we will evaluate the generalized analytic conditional Wiener and Feynman integrals of the functions $F$ in a Banach algebra which corresponds to Cameron-Storvick’s Banach algebra $𝒮$. Finally, we express the generalized analytic conditional Feynman...

In this paper, the authors introduce the notion of conditional expectation of an observable $x$ on a logic with respect to a sublogic, in a state $m$, relative to an element $a$ of the logic. This conditional expectation is an analogue of the expectation of an integrable function on a probability space.

For $C^{1,1}$ domains we give exact asymptotics near the domain’s boundary for the Green function and Martin kernel of the rotation invariant α-stable Lévy process. We also obtain a relative Fatou theorem for harmonic functions of the stable process.