THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH (Ⅱ)

The value distribution Of random analytic Dirichlet series of neutral growth has been' studied by the author on the assumption that the coefficients Of the series are martingaledifference sequence. This assumption is rather weak, and the result obtained in [1] concernsonly the value distribution with exception.The present paper deals with the Value distributioll, without exception, of random Dirichletseries when its coefficients are independent random variables with certain moment conditions…     

Point-Based Set-Valued Approximations,C -Differential Operators and Applications

In this article, we investigate the point-based set-valued approximation [H. Xu (1999). Set-valued approximation and Newton's methods. Mathematical Programming , 84 , 401-420.] and the C -differential operator [L. Qi (1996). C -Differential operators, C -differentiability and generalized Newton methods, Applied Mathematics Report, AMR96/5, School of Mathematics, The University of New South Wales, Sydney, Australia.] of a vector valued function. Several questions about C -differential operators posed in [L. Qi (1996). C -Differential operators, C -differentiability and generalized Newton methods, Applied Mathematics Report, AMR96/5, School of Mathematics, The University of New South Wales, Sydney, Australia.] are answered. Further, we discuss the application of C -differential operator in nonsmooth optimization. We derive optimality conditions and establish a mean value theorem in terms of convex C -differential operators. Finally, we propose a conceptual algorithm based on the convex C -differential operators.     

Graph algorithm for partially-linear problems obtained by absolute value functions

The increasing interest in partially-linear models is caused by their role in economics, technology and mathematics. Every continuous partially-linear function with a finite number of linear parts can be formulated by means of linear function and absolute value functions. If we presebt every absolote value function as vertex of a graph we obtain the graph interpretaion of this optimization problem. The Partially-linear problems are often not only nondifferentiable but nonconvex as well,which makes their solving by standard optimization methods difficult. In this work we give the necessary and sufficient conditions for local optimality. An algorithm for solving such problems, based on the constructive optimization methods is suggested.     

On the entropy minimization problem in Statistical Mechanics

In many works on Statistical Mechanics and Statistical Physics, when deriving the distribution of particles of ideal gases, one uses the method of Lagrange multipliers in a formal way. In this paper we treat rigorously this problem for Bose–Einstein, Fermi–Dirac and Maxwell–Boltzmann entropies and present a complete study in the case of the Maxwell–Boltzmann entropy. Our approach is based on recent results on series of convex functions.     

Convergence of a strong variational algorithm for relaxed controls involving a distributed optimal control problem of parabolic type 1

In this paper, we consider a class of Optimal Control problems involving first boundary value problems of parabolic type. A strong variational algorithm has been obtained for solving this class of optimal control problems in a paper by the author and D. W. Reid. It was also shown that any L∞ accumulation points of control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithm always have accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed control problem.     

Asymptotic results for conditional measures of association of a random sum

Asymptotic results are obtained for several conditional measures of association. The chosen random variables are the first two order statistics and the total sum within a random sum. Many of the results have confirmed the “one-jump” property of the risk model. Non-trivial limits are obtained when the dependence among the first two order statistics is considered. Our results help in understanding the extreme behaviour of well-known reinsurance treaties that involve only few large claims. Interestingly, the Pearson product-moment correlation coefficient between the first two order statistics provides an alternative procedure to estimate the tail index of the underlying distribution.     

MEASURING OPTIMAL CONNECTIONS IN LARGE NETWORKS: A NEW ALGORITHM AND ITS APPLICATIONS

Researchers have identified several problems in measuring the strongest path connecting pairs of actors in valued graphs. To address these problems, it has been proposed that average path value be used to indicate optimal connections between dyads. However, a lack of proper computer algorithm and its implementation has hindered a wide-range application of the proposed solution. In this paper we develop a computer algorithm and fully implement it with four JAVA programs, which are available on request. These programs produce an optimal connection matrix, which is subsequently inputted into UCINET for further multidimensional scaling and clustering analysis. We demonstrate this procedure with a data matrix containing 38 organizations in information technology. We discuss the methodological implications of the application of our algorithm to future social network studies.     

On pricing and reserving with-profits life insurance contracts

As a first approximation, asset and liability management issues faced by life insurance companies originate from the sale of with-profits contracts. These contracts are bond-type products with several rate guarantees and other interestsensitive embedded options. Benefits paid out to policyholders mostly depend on the investment performance of a given asset portfolio in which premiums are invested. Thus, guarantees and options granted to policyholders may become effective when the investment performance of the asset portfolio is poor. Issuing a with-profits contract is therefore not equivalent to issuing plain-vanilla debt. The purpose of this paper is to value with-profits liabilities in a consistent option-pricing framework and to develop efficient asset or liability strategies to manage profitability and variability of shareholder value.     

A note on constraint aggregation and value functions for two-stage stochastic integer programs

We consider a class of two-stage stochastic integer programs and their equivalent reformulation that uses the integer programming value functions in both stages. One class of solution methods in the literature is based on the idea of pre-computing and storing exact value functions, and then exploiting this information within a global branch-and-bound framework. Such methods are known to be very sensitive to the magnitude of feasible right-hand side values. In this note we propose a simple constraint-aggregation based approach that potentially alleviates this limitation.     

Information and preference reversals in lotteries

Several approaches have been proposed for evaluating information in expected utility theory. Among the most popular approaches are the expected utility increase, the selling price and the buying price. While the expected utility increase and the selling price always agree in ranking information alternatives, Hazen and Sounderpandian [11] have demonstrated that the buying price may not always agree with the other two. That is, in some cases, where the expected utility increase would value information A more highly than information B, the buying price may reverse these preferences. In this paper, we discuss the conditions under which all these approaches agree in a generic decision environment where the decision maker may choose to acquire arbitrary information bundles.