scholarly journals Some Resultats on Optimal Allocation of Policy Limits and Deductibles: Mixture Model

2021 ◽  
Vol 2 ◽  
pp. 4
Author(s):  
Bouhadjar Meriem ◽  
Halim Zeghdoudi ◽  
Abdelali Ezzebsa
Keyword(s):  
Mixture Model ◽  
Expected Utility ◽  
Scalar Product ◽  
Optimal Allocation ◽  
Stochastic Orders ◽  
Frequency Effect ◽  
Dependence Structure ◽  
Random Vectors ◽  
Scalar Products

The main purpose of this paper is to introduce and investigate stochastic orders of scalar products of random vectors. We study the problem of finding maximal expected utility for some functional on insurance portfolios involving some additional (independent) randomization. Furthermore, applications in policy limits and deductible are obtained, we consider the scalar product of two random vectors which separates the severity effect and the frequency effect in the study of the optimal allocation of policy limits and deductibles. In that respect, we obtain the ordering of the optimal allocation of policy limits and deductibles when the dependence structure of the losses is unknown. Our application is a further study of [1 − 6].

Ordering scalar products with applications in financial engineering and actuarial science

2016 ◽  
Vol 53 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Yinping You ◽  
Xiaohu Li
Keyword(s):  
Financial Engineering ◽  
Scalar Product ◽  
Joint Density ◽  
Actuarial Science ◽  
Random Vectors ◽  
Lower Tail ◽  
Scalar Products

Abstract In this paper we build the increasing convex (concave) order for the scalar product of random vectors with an upper (lower) tail permutation decreasing joint density. As applications, we revisit allocations of portfolio risks in financial engineering and of coverage limits and deductibles in insurance. Some related results in the literature are substantially updated.

scholarly journals Stochastic orderings of multivariate elliptical distributions

2021 ◽  
Vol 58 (2) ◽  
pp. 551-568
Author(s):  
Chuancun Yin
Keyword(s):  
Necessary Conditions ◽  
Stochastic Orders ◽  
Regularity Conditions ◽  
Elliptical Distributions ◽  
Multivariate Normal ◽  
Random Vectors ◽  
Stochastic Orderings ◽  
Sufficient And Necessary Conditions ◽  
New Inequalities ◽  
Unified Method

AbstractFor two n-dimensional elliptical random vectors X and Y, we establish an identity for $\mathbb{E}[f({\bf Y})]- \mathbb{E}[f({\bf X})]$, where $f\,{:}\, \mathbb{R}^n \rightarrow \mathbb{R}$ satisfies some regularity conditions. Using this identity we provide a unified method to derive sufficient and necessary conditions for classifying multivariate elliptical random vectors according to several main integral stochastic orders. As a consequence we obtain new inequalities by applying the method to multivariate elliptical distributions. The results generalize the corresponding ones for multivariate normal random vectors in the literature.

scholarly journals Pessimistic Portfolio Choice with One Safe and One Risky Asset and Right Monotone Probability Difference Order

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jiangfeng Li ◽  
Qiong Wu ◽  
Zhiqiang Ye ◽  
Shunming Zhang
Keyword(s):  
Portfolio Choice ◽  
Expected Utility ◽  
Comparative Statics ◽  
Risky Asset ◽  
Stochastic Orders ◽  
Monotone Likelihood Ratio ◽  
Changes In Risk ◽  
The Right ◽  
Monotone Probability ◽  
The Relationship

As is well known, a first-order dominant deterioration in risk does not necessarily cause a risk-averse investor to reduce his holdings of that deteriorated asset under the expected utility framework, even in the simplest portfolio setting with one safe asset and one risky asset. The purpose of this paper is to derive conditions on shifts in the distribution of the risky asset under which the counterintuitive conclusion above can be overthrown under the rank-dependent expected utility framework, a more general and prominent alternative of the expected utility. Two new criterions of changes in risk, named the monotone probability difference (MPD) and the right monotone probability difference (RMPD) order, are proposed, which is a particular case of the first stochastic dominance. The relationship among MPD, RMPD, and the other two important stochastic orders, monotone likelihood ratio (MLR) and monotone probability ratio (MPR), is examined. A desired comparative statics result is obtained when a shift in the distribution of the risky asset satisfies the RMPD criterion.

A short note on the dependence structure of random vectors

2019 ◽  
Vol 146 ◽  
pp. 200-205
Author(s):  
José M. González-Barrios ◽  
Eduardo Gutiérrez-Peña ◽  
Raúl Rueda
Keyword(s):  
Short Note ◽  
Dependence Structure ◽  
Random Vectors

scholarly journals Sparse regular variation

2021 ◽  
Vol 53 (4) ◽  
pp. 1115-1148
Author(s):  
Nicolas Meyer ◽  
Olivier Wintenberger
Keyword(s):  
Weak Convergence ◽  
Extreme Events ◽  
Spectral Measure ◽  
Regular Variation ◽  
Theoretical Framework ◽  
Efficient Algorithms ◽  
Dependence Structure ◽  
Random Vectors ◽  
Sparsity Structure ◽  
Natural Way

AbstractRegular variation provides a convenient theoretical framework for studying large events. In the multivariate setting, the spectral measure characterizes the dependence structure of the extremes. This measure gathers information on the localization of extreme events and often has sparse support since severe events do not simultaneously occur in all directions. However, it is defined through weak convergence, which does not provide a natural way to capture this sparsity structure. In this paper, we introduce the notion of sparse regular variation, which makes it possible to better learn the dependence structure of extreme events. This concept is based on the Euclidean projection onto the simplex, for which efficient algorithms are known. We prove that under mild assumptions sparse regular variation and regular variation are equivalent notions, and we establish several results for sparsely regularly varying random vectors.

scholarly journals An efficient secure sum of multi-scalar products protocol base on elliptic curve

2022 ◽  
Vol 2 (14) ◽  
pp. 18-25
Author(s):  
Vu Thi Van ◽  
Luong The Dung ◽  
Hoang Van Quan ◽  
Tran Thi Luong
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Scalar Product ◽  
Recommendation System ◽  
Statistical Data ◽  
Privacy Preserving ◽  
Secure Computation ◽  
Statistical Data Analysis ◽  
Privacy Preserving Data Mining ◽  
Scalar Products

The secure scalar product protocol is widely applied to solve practical problems such as privacy-preserving data mining, secure auction, secure electronic voting, privacy-preserving recommendation system, privacy-preserving statistical data analysis, etc.. In this paper, we propose an efficient multi-party secure computation protocol using Elliptic curve cryptography, which allows to compute the sum value of multi-scalar products without revealing about the input vectors. Moreover, theoretical and experimental analysis shows that the proposed method is more efficient than others in both computation and communication.

scholarly journals Supermodular ordering of Poisson and binomial random vectors by tree-based correlations

2018 ◽  
Vol 38 (2) ◽  
pp. 385-405
Author(s):  
Nicolas Privault ◽  
Bünyamin Kizildemir
Keyword(s):  
Random Variables ◽  
Covariance Matrices ◽  
Binary Trees ◽  
Independent Random Variables ◽  
Dependence Structure ◽  
Random Vectors ◽  
Partially Ordered ◽  
Ordered Trees ◽  
Lévy Measures ◽  
Inversion Techniques

We construct a dependence structure for binomial, Poisson and Gaussian random vectors, based on partially ordered binary trees and sums of independent random variables. Using this construction, we characterize the supermodular ordering of such random vectors via the componentwise ordering of their covariance matrices. For this, we apply Möbius inversion techniques on partially ordered trees, which allow us to connect the Lévy measures of Poisson random vectors on the discrete d-dimensional hypercube to their covariance matrices.

scholarly journals Ruin Problems of Multidimensional Risk Models under Constant Interest Rates and Dependent Risks with Heavy Tails

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Xinmei Shen ◽  
Meng Yuan ◽  
Dawei Lu
Keyword(s):  
Interest Rates ◽  
Ruin Probability ◽  
Heavy Tails ◽  
Optimal Allocation ◽  
Risk Model ◽  
Dependence Structure ◽  
Asymptotic Estimates ◽  
Risk Models ◽  
Dependent Risks ◽  
Constant Interest

Consider a discrete-time multidimensional risk model with constant interest rates where capital transfers between lines are partially allowed over each period. By assuming a large initial capital and regularly varying distributions for the losses, we derive asymptotic estimates for the ruin probability under some dependence structure and study the optimal allocation of the initial reserve. Some numerical simulations are provided to illuminate our main results.

scholarly journals CONSTRUCTION OF MONODROMY MATRIX IN THE F-BASIS AND SCALAR PRODUCTS IN SPIN CHAINS

2001 ◽  
Vol 16 (12) ◽  
pp. 2175-2193 ◽  
Author(s):  
A. A. OVCHINNIKOV
Keyword(s):  
Scalar Product ◽  
Monodromy Matrix ◽  
Quantum Spin ◽  
Matrix Elements ◽  
Quantum Spin Chain ◽  
Usual Basis ◽  
The Matrix ◽  
General Scalar ◽  
Scalar Products

We present in a simple terms the theory of the factorizing operator introduced recently by Maillet and Sanches de Santos for the spin-1/2 chains. We obtain the explicit expressions for the matrix elements of the factorizing operator in terms of the elements of the monodromy matrix. We use this results to derive the expression for the general scalar product for the quantum spin chain. We comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state. We also establish the direct correspondence between the calculations of scalar products in the F-basis and the usual basis.

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