Premium evaluation for different loss distributions using utility theory

Harman Preet Singh Kapoor; Kanchan Jain

Displaying similar documents to “Premium evaluation for different loss distributions using utility theory”

On asymmetric distributions of copula related random variables which includes the skew-normal ones

Ayyub Sheikhi, Fereshteh Arad, Radko Mesiar (2022)

Kybernetika

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Assuming that $C_{X, Y}$ is the copula function of $X$ and $Y$ with marginal distribution functions $F_{X} (x)$ and $F_{Y} (y)$ , in this work we study the selection distribution $Z \overset{d}{=} (X | Y \in T)$ . We present some special cases of our proposed distribution, among them, skew-normal distribution as well as normal distribution. Some properties such as moments and moment generating function are investigated. Also, some numerical analysis is presented for illustration.

Global approximations for the γ-order Lognormal distribution

Thomas L. Toulias (2013)

Discussiones Mathematicae Probability and Statistics

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A generalized form of the usual Lognormal distribution, denoted with $_{γ}$ , is introduced through the γ-order Normal distribution $_{γ}$ , with its p.d.f. defined into (0,+∞). The study of the c.d.f. of $_{γ}$ is focused on a heuristic method that provides global approximations with two anchor points, at zero and at infinity. Also evaluations are provided while certain bounds are obtained.

A depth-based modification of the k-nearest neighbour method

Ondřej Vencálek, Daniel Hlubinka (2021)

Kybernetika

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We propose a new nonparametric procedure to solve the problem of classifying objects represented by $d$ -dimensional vectors into $K \geq 2$ groups. The newly proposed classifier was inspired by the $k$ nearest neighbour (kNN) method. It is based on the idea of a depth-based distributional neighbourhood and is called $k$ nearest depth neighbours (kNDN) classifier. The kNDN classifier has several desirable properties: in contrast to the classical kNN, it can utilize global properties of the considered...

The right tail exponent of the Tracy–Widom $β$ distribution

Laure Dumaz, Bálint Virág (2013)

Annales de l'I.H.P. Probabilités et statistiques

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The Tracy–Widom $β$ distribution is the large dimensional limit of the top eigenvalue of $β$ random matrix ensembles. We use the stochastic Airy operator representation to show that as $a \to \infty$ the tail of the Tracy–Widom distribution satisfies $P ({𝑇𝑊}_{β} g t; a) = a^{- (3 / 4) β + o (1)} exp (- \frac{2}{3} β a^{3 / 2}) .$

Local equivalence of some maximally symmetric $(2, 3, 5)$ -distributions II

Matthew Randall (2025)

Archivum Mathematicum

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We show the change of coordinates that maps the maximally symmetric $(2, 3, 5)$ -distribution given by solutions to the $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy equation to the flat Cartan distribution. This establishes the local equivalence between the maximally symmetric $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy distribution and the flat Cartan or Hilbert-Cartan distribution. We give the set of vector fields parametrised by solutions to the $k = \frac{2}{3}$ and $k = \frac{3}{2}$ generalised Chazy equation and the corresponding Ricci-flat conformal scale...

Scale-free percolation

Maria Deijfen, Remco van der Hofstad, Gerard Hooghiemstra (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We formulate and study a model for inhomogeneous long-range percolation on $ℤ^{d}$ . Each vertex $x \in ℤ^{d}$ is assigned a non-negative weight $W_{x}$ , where ${(W_{x})}_{x \in ℤ}^{d}$ are i.i.d. random variables. Conditionally on the weights, and given two parameters $α, λ g t; 0$ , the edges are independent and the probability that there is an edge between $x$ and $y$ is given by $p_{x y} = 1 - exp {- λ W_{x} W_{y} {/ | x - y |}^{α}}$ . The parameter $λ$ is the percolation parameter, while $α$ describes the long-range nature of the model. We focus on the degree distribution in the resulting graph, on whether...

Geometrically strictly semistable laws as the limit laws

Marek T. Malinowski (2007)

Discussiones Mathematicae Probability and Statistics

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A random variable X is geometrically infinitely divisible iff for every p ∈ (0,1) there exists random variable $X_{p}$ such that $X \overset{d}{=} \sum_{k = 1}^{T (p)} X_{p, k}$ , where $X_{p, k}$ ’s are i.i.d. copies of $X_{p}$ , and random variable T(p) independent of $X_{p, 1}, X_{p, 2}, . . .$ has geometric distribution with the parameter p. In the paper we give some new characterization of geometrically infinitely divisible distribution. The main results concern geometrically strictly semistable distributions which form a subset of geometrically infinitely divisible distributions....

On Lagrangian systems with some coordinates as controls

Franco Rampazzo (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Let $\Sigma$ be a constrained mechanical system locally referred to state coordinates $(q^{1},...,q^{N},\gamma^{1},...,\gamma^{M})$ . Let $(\tilde{\gamma}^{1}...\tilde{\gamma}^{M})(\cdot)$ be an assigned trajectory for the coordinates $\gamma^{\alpha}$ and let $u(\cdot)$ be a scalar function of the time, to be thought as a control. In [4] one considers the control system $\Sigma_{\hat{\gamma}}$ , which is parametrized by the coordinates $(q^{1},...,q^{N})$ and is obtained from $\Sigma$ by adding the time-dependent, holonomic constraints $\gamma^{\alpha}=\hat{\gamma}^{\alpha}(t):=\tilde{\gamma}^{\alpha}(u(t))$ . More generally, one can consider a vector-valued control $u(\cdot)=(u^{1},...,u^{M})(\cdot)$ which is directly identified with $\hat{\gamma}(\cdot)=(\hat{\gamma}^{1},...,\hat{\gamma}^{M})(\cdot)$ . If one denotes the momenta...

On control theory and its applications to certain problems for Lagrangian systems. On hyperimpulsive motions for these. II. Some purely mathematical considerations for hyper-impulsive motions. Applications to Lagrangian systems

Aldo Bressan (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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See Summary in Note I. First, on the basis of some results in [2] or [5]-such as Lemmas 8.1 and 10.1-the general (mathematical) theorems on controllizability proved in Note I are quickly applied to (mechanic) Lagrangian systems. Second, in case $\Sigma$ , $\chi$ and $M$ satisfy conditions (11.7) when $\mathcal{Q}$ is a polynomial in $\dot{\gamma}$ , conditions (C)-i.e. (11.8) and (11.7) with $\mathcal{Q}\equiv 0$ -are proved to be necessary for treating satisfactorily $\Sigma$ 's hyper-impulsive motions (in which positions can suffer first order discontinuities)....

Construction methods for gaussoids

Tobias Boege, Thomas Kahle (2020)

Kybernetika

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The number of $n$ -gaussoids is shown to be a double exponential function in $n$ . The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing $3$ -minors and encoding the resulting combinatorial constraints in a suitable transitive graph. Various special classes of gaussoids arise from restricting the allowed $3$ -minors.

Some new Formulas involving $Γ_{q}$ Functions

Thomas Ernst (2007)

Rendiconti del Seminario Matematico della Università di Padova

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Perron-Frobenius operators and the Klein-Gordon equation

Francisco Canto-Martín, Håkan Hedenmalm, Alfonso Montes-Rodríguez (2014)

Journal of the European Mathematical Society

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For a smooth curve $Γ$ and a set $Λ$ in the plane $ℝ^{2}$ , let $A C (Γ; Λ)$ be the space of finite Borel measures in the plane supported on $Γ$ , absolutely continuous with respect to the arc length and whose Fourier transform vanishes on $Λ$ . Following [12], we say that $(Γ, Λ)$ is a Heisenberg uniqueness pair if $A C (Γ; Λ) = {0}$ . In the context of a hyperbola $Γ$ , the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets $Λ$ of a collection of solutions to the Klein-Gordon equation. In this work, we mainly...

Gap universality of generalized Wigner and $β$ -ensembles

László Erdős, Horng-Tzer Yau (2015)

Journal of the European Mathematical Society

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We consider generalized Wigner ensembles and general $β$ -ensembles with analytic potentials for any $β \geq 1$ . The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian $β$ -ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal....

Characterization of functions whose forward differences are exponential polynomials

J. M. Almira (2017)

Commentationes Mathematicae Universitatis Carolinae

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Given ${h_{1}, \dots, h_{t}}$ a finite subset of $ℝ^{d}$ , we study the continuous complex valued functions and the Schwartz complex valued distributions $f$ defined on $ℝ^{d}$ with the property that the forward differences $Δ_{h_{k}}^{m_{k}} f$ are (in distributional sense) continuous exponential polynomials for some natural numbers $m_{1}, \dots, m_{t}$ .

Universal rates for estimating the residual waiting time in an intermittent way

Gusztáv Morvai, Benjamin Weiss (2020)

Kybernetika

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A simple renewal process is a stochastic process ${X_{n}}$ taking values in ${0, 1}$ where the lengths of the runs of $1$ ’s between successive zeros are independent and identically distributed. After observing $X_{0}, X_{1}, ... X_{n}$ one would like to estimate the time remaining until the next occurrence of a zero, and the problem of universal estimators is to do so without prior knowledge of the distribution of the process. We give some universal estimates with rates for the expected time to renewal as well as for the conditional...

An example of a reflexive Lorentz Gamma space with trivial Boyd and Zippin indices

Alexei Karlovich, Eugene Shargorodsky (2021)

Czechoslovak Mathematical Journal

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We show that for every $p \in (1, \infty)$ there exists a weight $w$ such that the Lorentz Gamma space $Γ_{p, w}$ is reflexive, its lower Boyd and Zippin indices are equal to zero and its upper Boyd and Zippin indices are equal to one. As a consequence, the Hardy-Littlewood maximal operator is unbounded on the constructed reflexive space $Γ_{p, w}$ and on its associate space $Γ_{p, w}^{'}$ .

Properties of unique information

Johannes Rauh, Maik Schünemann, Jürgen Jost (2021)

Kybernetika

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We study the unique information function $U I (T : X ∖ Y)$ defined by Bertschinger et al. within the framework of information decompositions. In particular, we study uniqueness and support of the solutions to the convex optimization problem underlying the definition of $U I$ . We identify sufficient conditions for non-uniqueness of solutions with full support in terms of conditional independence constraints and in terms of the cardinalities of $T$ , $X$ and $Y$ . Our results are based on a reformulation of the first...