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 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].

scholarly journals Permutation Monotone Functions of Random Vectors with Applications in Financial and Actuarial Risk Management

2015 ◽  
Vol 47 (01) ◽  
pp. 270-291 ◽  
Author(s):  
Xiaohu Li ◽  
Yinping You
Keyword(s):  
Financial Engineering ◽  
Capital Allocation ◽  
Portfolio Allocation ◽  
Monotone Functions ◽  
Insurance Policy ◽  
Actuarial Science ◽  
Unified Approach ◽  
Actuarial Risk ◽  
Increasing Functions ◽  
Theoretical Results

In this paper we develop two permutation theorems on argument increasing functions of a multivariate random vector and a real parameter vector. We use the unified approach of our two theorems to provide some important theoretical results on the capital allocation in actuarial science, the deductible and upper limit allocations in insurance policy, and portfolio allocation in financial engineering. Our results successfully improve or extend the corresponding works in the literature.

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 Marginal Distributions of Random Vectors Generated by Affine Transformations of Independent Two-Piece Normal Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Maximiano Pinheiro
Keyword(s):  
Probability Density ◽  
Distribution Functions ◽  
Joint Density ◽  
Cumulative Distribution ◽  
Marginal Probability ◽  
Affine Transformations ◽  
Skewed Distributions ◽  
Random Vectors ◽  
Marginal Distributions ◽  
Cumulative Distribution Functions

Marginal probability density and cumulative distribution functions are presented for multidimensional variables defined by nonsingular affine transformations of vectors of independent two-piece normal variables, the most important subclass of Ferreira and Steel's general multivariate skewed distributions. The marginal functions are obtained by first expressing the joint density as a mixture of Arellano-Valle and Azzalini's unified skew-normal densities and then using the property of closure under marginalization of the latter class.

scholarly journals Permutation Monotone Functions of Random Vectors with Applications in Financial and Actuarial Risk Management

2015 ◽  
Vol 47 (1) ◽  
pp. 270-291 ◽  
Author(s):  
Xiaohu Li ◽  
Yinping You
Keyword(s):  
Financial Engineering ◽  
Capital Allocation ◽  
Portfolio Allocation ◽  
Monotone Functions ◽  
Insurance Policy ◽  
Actuarial Science ◽  
Unified Approach ◽  
Actuarial Risk ◽  
Increasing Functions ◽  
Theoretical Results

In this paper we develop two permutation theorems on argument increasing functions of a multivariate random vector and a real parameter vector. We use the unified approach of our two theorems to provide some important theoretical results on the capital allocation in actuarial science, the deductible and upper limit allocations in insurance policy, and portfolio allocation in financial engineering. Our results successfully improve or extend the corresponding works in the literature.

scholarly journals A characterization of matrix variate normal distribution

1994 ◽  
Vol 17 (2) ◽  
pp. 341-346 ◽  
Author(s):  
Khoan T. Dinh ◽  
Truc T. Nguyen
Keyword(s):  
Linear Regression ◽  
Normal Distribution ◽  
Covariance Matrix ◽  
The Other ◽  
Joint Density ◽  
Random Vectors

The joint normality of two random vectors is obtained based on normal conditional with linear regression and constant covariance matrix of each vector given the value of the other without assuming the existence of the joint density. This result is applied to a characterization of matrix variate normal distribution.

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.

scholarly journals Invariant Scalar Product and Associated Structures for Tachyonic Klein–Gordon Equation and Helmholtz Equation

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1302
Author(s):  
Francisco F. López-Ruiz ◽  
Julio Guerrero ◽  
Victor Aldaya
Keyword(s):  
Helmholtz Equation ◽  
Scalar Product ◽  
Gordon Equation ◽  
Invariance Group ◽  
Unified Framework ◽  
Property A ◽  
Oscillatory Solutions ◽  
Klein Gordon ◽  
Scalar Products ◽  
Klein Gordon Equation

Although describing very different physical systems, both the Klein–Gordon equation for tachyons (m2<0) and the Helmholtz equation share a remarkable property: a unitary and irreducible representation of the corresponding invariance group on a suitable subspace of solutions is only achieved if a non-local scalar product is defined. Then, a subset of oscillatory solutions of the Helmholtz equation supports a unirrep of the Euclidean group, and a subset of oscillatory solutions of the Klein–Gordon equation with m2<0 supports the scalar tachyonic representation of the Poincaré group. As a consequence, these systems also share similar structures, such as certain singularized solutions and projectors on the representation spaces, but they must be treated carefully in each case. We analyze differences and analogies, compare both equations with the conventional m2>0 Klein–Gordon equation, and provide a unified framework for the scalar products of the three equations.

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