Monte Carlo versus Numerical Convolutions: Some Critical Remarks

Article Abstract:

Computer methodology for assisting in actuarial problems is considered. In this research, the computer is regarded only as calculation equipment. Initially, a problem is developed in a logical sense for the computer, and calculations or approximations ensue. In this case Monte Carlo simulation was preferred, although it is not always exact. A hypothetical situation based on a life insurance firm's portfolio of policies is given to demonstrate the numerical processes involved in middle stages of the process. Algorithms and discrete density considerations are delineated. Tables of numerical convolution data are included, as is an algorithm for general convolution calculations.

Computers, Laws, regulations and rules, Digital computers

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K-Tree/K-Subgraph: a program package for minimal weighted K-cardinality trees and subgraphs

Article Abstract:

The K-Tree/K-Subgraph package is an implementation of several algorithms and heuristics for solving the minimal weighted K-cardinality tree and subgraph problem. K-Tree contains two branch-and-bound schemes written in Turbo-Pascal 5.0. KTreecut, the second program, presents a branch-and-cut algorithm in C on an IBM-RS 6000 under operating system AIX 3.1. K-Sub contains heuristic algorithms while KSubcut is the exact algorithm for the K-cardinality subgraph problem.

Usage, Software, Branch and bound algorithms

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An axiomatic characterization of some locations in trees

Article Abstract:

Several axioms are proposed for characterizing the absolute median and squared median of a tree. The axioms are based on the Consistency axiom of the first type used in characterizing a voting procedure called Borda's rule. They focus on the objective function of the tree rather than the location obtained via an optimization scheme. The axioms can be used in diverse topics such as the aggregation of expert opinions and the measurement of inequality.

Analysis, Evaluation, Axioms

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