具有高安全性和有效性的Ⅱ期两阶段临床试验

Ⅱ期临床试验的主要目的是对药物治疗的安全性和有效性进行评估.针对具有高安全性的Ⅱ期两阶段临床试验,给出小样本量下关于安全性和有效性的精确检验方法,并证明最大Ⅰ类错误概率与Ⅱ类错误概率分别在原假设和备择假设的边界处达到.在期望样本量最小原则下,给出最优两阶段设计的构造方法和常用设计表,供实际应用选用.     

The fundamental theorem of mutual insurance

The essence of mutual insurance is the notion that re-distributing risk in a pool of risks is more beneficial than taking the risk alone. Interpreting ‘more beneficial’ as an increase in utility and considering sequences of exchangeable risks, we are able to formalize this notion from the policyholder’s perspective and demonstrate its validity for various alternative preference functionals (e.g., expected utility, Choquet expected utility, and distortion risk measures). To obtain this result, we exploit that for a sequence of exchangeable risks the corresponding sequence of arithmetical averages is a reversed martingale.We conclude that pooling risks is fundamental for understanding the mechanisms of insurance because it favourably affects the utility of policyholders, and we refer to this phenomenon as the ‘utility-improving effect of risk pooling’. Moreover, we demonstrate that the utility of the policyholder is (strictly) increasing with the size of the risk pool.     

The valuation of life contingencies: A symmetrical triangular fuzzy approximation

This paper extends the framework for the valuation of life insurance policies and annuities by Andrés-Sánchez and González-Vila (2012, 2014) in two ways. First we allow various uncertain magnitudes to be estimated by means of fuzzy numbers. This applies not only to interest rates but also to the amounts to be paid out by the insurance company. Second, the use of symmetrical triangular fuzzy numbers allows us to obtain expressions for the pricing of life contingencies and their variability that are closely linked to standard financial and actuarial mathematics. Moreover, they are relatively straightforward to compute and understand from a standard actuarial point of view.     

Utility maximization problem with random endowment and transaction costs: when wealth may become negative

In this article, we study the problem of maximizing expected utility from the terminal wealth with proportional transaction costs and random endowment. In the context of the existence of consistent price systems, we consider the duality between the primal utility maximization problem and the dual one, which is set up on the domain of finitely additive measures. In particular, we prove duality results for utility functions supporting possibly negative values. Moreover, we construct a shadow market by the dual optimal process and consider the utility-based pricing for random endowment.     

Optimal proportional reinsurance with common shock dependence

In this paper, we consider the optimal proportional reinsurance strategy in a risk model with multiple dependent classes of insurance business, which extends the work of Liang and Yuen (2014) to the case with the reinsurance premium calculated under the expected value principle and to the model with two or more classes of dependent risks. Under the criterion of maximizing the expected exponential utility, closed-form expressions for the optimal strategies and value function are derived not only for the compound Poisson risk model but also for the diffusion approximation risk model. In particular, we find that the optimal reinsurance strategies under the expected value premium principle are very different from those under the variance premium principle in the diffusion risk model. The former depends not only on the safety loading, time and interest rate, but also on the claim size distributions and the counting processes, while the latter depends only on the safety loading, time and interest rate. Finally, numerical examples are presented to show the impact of model parameters on the optimal strategies.     

Determination/estimation of an optimal replacement interval under minimal repair

In this paper the problem of estimation of an optimal replacement interval for a system which is minimally repaired at failures is studied. The problem is investigated both under a parametric and a nonparametric form of the failure intensity of the system. It is assumed that observational data from n systems are available. Some asymptotic results are shown. A graphical procedure for determining/estimating an optimal replacement interval is presented. The procedure is particularly valuable for sensitivity analyses, for example with respect to the costs involved.     

Solving stochastic convex feasibility problems in hilbert spaces

In a stochastic convex feasibility problem connected with a complete probability space (Ω,A,μ) and a family of closed convex sets (C_ω)_ωεΩ in a real Hilbert space H, one wants to find a point that belongs to C_ω for μ almost all ω ε Ω. We present a projection based method where the variable relaxation parameter is defined by a geometrical condition, leading to an iteration sequence that is always weakly convergent to a μ almost common point. We then give a general condition assuring norm convergence of this equation to that μ almost common point     

A model of product line design and introduction sequence with reservation utility

Cannibalization is a major concern for a firm when designing a product line. In addition, external options from outside the firm’s product line may also play a significant role. In this paper, we investigate the impact of external options, represented by reservation utility, on product line design and introduction sequence. We find that: (a) heterogeneous reservation utility defines the relative attractiveness of segments and corresponding product line; (b) reservation utility makes it more favorable to introduce products sequentially rather than simultaneously; (c) aggregating segments is an effective way to mitigate cannibalization when it becomes too difficult to manage with different values of reservation utility across multiple segments; and (d) introducing products in a non-monotone order of quality can improve profit from simultaneous introduction when the value of reservation utility of a middle segment is particularly high.     

绿色建筑项目管理综合均衡优化研究

绿色建筑凭借其诸多优点,已然成为我国未来建筑发展的新方向,而对绿色建筑的工期、成本和功能进行全面系统研究并进行综合均衡优化,对于促进绿色建筑的发展具有深远影响.在描述各工程活动的成本和持续时间之间、功能和持续时间之间的非线性关系基础上,运用多属性效用函数理论构建了绿色建筑项目的功能一工期一成本综合均衡优化模型,并用遗传算法进行求解,可以得到最佳均衡解.最后通过一个实例验证了优化模型具有良好的科学性和实用性.     

ON EQUILIBRIUM PRICING AS CONVEX OPTIMIZATION

We study competitive economy equilibrium computation. We show that, for the first time, the equilibrium sets of the following two markets： 1. A mixed Fisher and Arrow- Debreu market with homogeneous and log-concave utility functions; 2. The Fisher and Arrow-Debreu markets with several classes of concave non-homogeneous utility functions; are convex or log-convex. Furthermore, an equilibrium can be computed as convex opti- mization by an interior-point algorithm in polynomial time.