A statistical approach to graduation by mathematical formula

Graduation by mathematical formula is recast as problem of statistical estimation. The method of maximum likelihood is used to determine the estimates of the parameters. Theory is developed to allow for estimation without resorting to the usual ‘exposure’ formulas. Both single and multiple decrement models are considered. Theoretical results are obtained for some specific mortality models. Numerical procedures to obtain the estimates are considered.     

New approaches to statistical learning theory

We present new tools from probability theory that can be applied to the analysis of learning algorithms. These tools allow to derive new bounds on the generalization performance of learning algorithms and to propose alternative measures of the complexity of the learning task, which in turn can be used to derive new learning algorithms.     

Bayesian graduation of FHA/HUD single-family home mortgage insurance contracts — Section 203

In this paper we will describe a procedure used to construct the survivorship (or double-decrement) table for FHA Section 203 mortgage insurance contracts on single-family home mortgages having a 30-year term. The methodological approach is based on a procedure known in the actuarial literature as Bayesian graduation. This procedure has been described by Kimeldorf and Jones (1967) and Hickman and Miller (1977).     

On the solution of some (parametric) linear complementarity problems with applications to portfolio selection,structural engineering and actuarial graduation

In this paper we discuss three applications of a class of (parametric) linear complementarity problems arising independently from such diverse areas as portfolio selection, structural engineering and actuarial graduation. After explaining how the complementarity problems emerge in these applications, we perform some analytical comparisons (based on operation counts and storage requirements) of several existing algorithms for solving this class of complementarity problems. We shall also present computational results to support the analytical comparisons. Finally, we deduce some conclusions about the general performance of these algorithms.This research is supported in part by the United States Army under Contract No. DAAG29-75-C-0024, the National Science Foundation under Grant No. MCS75-17385 and Grant ENG77-11136.     

A contribution to the theory of condition

Summary In this paper the use of the condition number of a problem, as defined by Rice in 1966, is discussed. For the eigenvalue, eigenvector, and linear least squares problems either condition numbers according to various norms are determined or lower and upper bounds for them are derived.     

A representation theory for the impulse control of jump processes

A state space representation theory for the impulse control of a quite general class of non-Markov jump processes is developed. Control decisions are based upon observations of past histories of an input jump process and observations of the current state of the corresponding controlled output. A verification theorem establishes that a solution of a system of quasi variational inequalities gives rise naturally to an optimal impulse policy. The proof of optimality relies upon an extended version of the well-known Dynkin formula for Markov processes.     

A contribution to the theory of Maxwell fluids. II

The local classical unique solvability of the periodic initial-boundary problem and of the cauchy problem is proved for the nonstationary quasilinear system describing the motion of Maxwell fluids.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 131, pp. 106–113, 1983.     

Bayesian graduation of mortality rates: An application to reserve evaluation

This paper presents Bayesian graduation models of mortality rates, using Markov chain Monte Carlo (MCMC) techniques. Graduated annual death probabilities are estimated through the predictive distribution of the number of deaths, which is assumed to follow a Poisson process, considering that all individuals in the same age class die independently and with the same probability. The resulting mortality tables are formulated through dynamic Bayesian models. Calculation of adequate reserve levels is exemplified, via MCMC, making use of the value at risk concept, demonstrating the importance of using “true” observed mortality figures for the population exposed to risk in determining the survival coverage rate.     

A nonalgebraic approach to the theory of linear topological spaces

The basic theory developed in the setting of an algebraic system endowed with a topology which renders the operations continuous (e.g. a topological linear space) can be produced entirely by geometric (set-theoretic) notions without using algebra. This theory affords an interesting synthesis of classical results, and is more general. For example, our theory applies to a larger class of spaces than linear topological spaces, but is powerful enough to prove the appropriate formulation in this setting of the Krein-Milman theorem on extreme points. This theorem is the goal of this particular article, as an example of the direction which the theory can be made to take.     

A contribution to the theory of singular integral equations with carleman shift

Let the operator N be defined by . It is shown that in the spaces L^P(R_ü;h) (h(x) = x^o|x+i|; -1<_oo+相似文献   

Construction of linear response theory for classical systems by the nonequilibrium statistical operator method

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 80, No. 3, pp. 452–460, September, 1989.     

A contribution to shape theory for the ising model at low temperature

Summary We consider low temperature limits of Gibbs states of the ferromagnetic nearest-neighbour Ising Hamiltonian in the positive orthant of the lattice ^d ,d=1, 2,..., under a negative boundary condition and a small positive external fieldh that decreases linearly with the temperatureT. It is shown that positive and negative spins are separated by a staircase-shaped random boundary. Its explicit distribution is computed in the case that the ratio =h/T exceeds some positive ₀. For < ₀, our results do not rule out infinite negative areas.