The recent financial deregulation and internationalization have caused a great deal of financial risk to banking in Japan. Therefore financial risk management becomes very important, and banks need to manage not only profit, but also risk. Several models relating to the bank management have been studied as mathematical programming problems in finance literatures. Risk measures are variously defined, however there are no models based on the idea of risk management (ALM). Therefore we propose the risk measure based on ALM, and the mathematical programming model approach with them. Then goal programming, which is one of the mathematical programming, is applied to the model, in order to manage profit and risk by setting their aspiration levels and required levels and to represent the trade-off relation between profit and risk. In this model, the management is assumed to have three kinds of conflicting goals, which are the goals of (i) interest rate risk exposure, (ii) profit, and (iii) maturity gap for active risk management (which means taking actively the risk based on expecting the trend of the interest rate). In addition to these specific goals, regulations, policy on banking and market conditions have to be considered. The four kinds of constraints are formulated, which are the constraints of (i) the upper limit of liquidity risk exposure, (ii) the lower limit of risk asset ratio, (iii) the lower limit of the ratio of cash to deposit, and (iv) the upper and/or the lower bounds of feasible funding, investment, and so on. Finally, several numerical examples are analyzed in order to investigate the performance of the approach. Due to space restriction, we describe two examples, which are (i) solved in various kinds of goal levels, and (ii) solved in different expectation to the trend of interest rate, in this paper. The results presented are. so remarkably good that the model provides a very real advance over previously reported models.

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We present a potential reduction algorithm which performs at most one rank one update at each iteration and at most O(nL) updates to solve a linear program. This algorithm requires O(n^3L) arithmetic operations. An important aspect of this algorithm and its analysis is that it does not always require the approximate scaling matrix to be in a certain box around the primal-dual scaling matrix.

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We propose a separating-hyperplane algorithm for finding a nearest pair of points in two polytopes, where each polytope is expressed as the convex hull of given points in a Euclidian space. The proposed algorithm is an extension of the authors dual algorithm for finding the minimum-norm point in a polytope.

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A word processor has become one of essential devices used in offices. Document files created by using a word processor are generally preserved on a floppy disk or floppy disks for references. Nevertheless, the files stored on a floppy disk are occasionally lost due to human errors, the life of the floppy disk and a failure of hardware devices, which comprise the word processor. This is called a floppy disk failure. One of the simplest methods for protecting us from such serious losses is to backup files on another floppy disk. Frequent backup operations would spend much time in themselves although they could reduce the loss at a floppy disk failure. On the contrary, occasional backup operations would make the loss at a floppy disk failure very large although they could save time in backup operations. These observations reveal the significance of determining an adequate backup timing of files. The present study proposes a 1/N backup policy for data floppy disks, which suggest to backup files when 1/N of the total memory of a floppy disk is consumed. The availability of the proposed backup policy is formulated as an objective function under efficiency basis. The existence of an optimal integer N^* that maximizes the availability is then examined to clarify the conditions under which such an optimal integer exists. Numerical examples are also presented.

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We want to select a good one from among n candidates. Taking the cost of interview into consideration, we determine an optimum number i, take a random sample of size i and choose the best one out of the sample. The probability distribution of the absolute rank r of the chosen individual is obtained. After a fundamental theory is developed, the asymptotic theories are considered when n becomes very large, for the cases of high, medium, and low cost.

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