Utility Functions

Abstract

This article is a self-contained survey of utility functions and some of their applications. Throughout the paper the theory is illustrated by three examples: exponential utility functions, power utility functions of the first kind (such as quadratic utility functions), and power utility functions of the second kind (such as the logarithmic utility function). The postulate of equivalent expected utility can be used to replace a random gain by a fixed amount and to determine a fair premium for claims to be insured, even if the insurer’s wealth without the new contract is a random variable itself. Then n companies (or economic agents) with random wealth are considered. They are interested in exchanging wealth to improve their expected utility. The family of Pareto optimal risk exchanges is characterized by the theorem of Borch. Two specific solutions are proposed. The first, believed to be new, is based on the synergy potential; this is the largest amount that can be withdrawn from the system without hurting any company in terms of expected utility. The second is the economic equilibrium originally proposed by Borch. As by-products, the option-pricing formula of Black-Scholes can be derived and the Esscher method of option pricing can be explained.     

Cost-utility analysis of the rehabilitation of patients with musculoskeletal problems

The objective of this study is to discuss the rehabilitation of patients in primary health care with problems in the musculoskeletal system from a socioeconomic perspective. A trial with coordinated rehabilitation in primary health care is compared with traditional rehabilitation. This trial, performed in Sweden in 1994, was a two-year prospective and comparative study of consecutively included patients with long-term illnesses due musculoskeletal problems (810 observations). A cost-utility analysis shows that the new rehabilitation program in primary health care is a cost-minimization program for society. There is no significant difference in the quality of life between the trial and control groups. The total cost is lower for rehabilitation in primary health care than for traditional rehabilitation (6 percent). The indirect costs are higher than the direct health care costs (60 percent), and payments from social insurance increased by 8 percent. The health economic results support rehabilitation in primary health care but also points out that this type of rehabilitation can be further improved.     

Knowledge transfer in project‐based organizations: An organizational culture perspective

This conceptual paper investigates the process of knowledge transfer in project‐based organizations from the perspective of organizational culture. The paper identifies obstacles to knowledge transfer in project‐based organizations and emphasizes the importance of organizational and project cultures in this process. The study provides some suggestions for improving knowledge transfer in project‐based organizations and notes the implications of the paper for project management.     

均匀圆阵的测向模糊研究

在高分辨阵列测向系统中,均匀圆阵(UCA)是一种广泛使用的阵列结构。利用均匀圆阵的阵列流形的微分几何作为分析工具,对实际中常用的几种均匀圆阵的测向模糊进行了大量的计算机仿真试验,定量地给出了这些阵列的测向模糊方向和相应的秩,揭示了均匀圆阵的测向模糊性能与其阵元数和孔径之间的关系,得出了一些有实际意义的结论。这对工程应用时均匀圆阵的选择和构造具有很强的参考价值和指导意义,可以避免系统设计的盲目性和随意性。