Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks

In this paper, we investigate an optimal reinsurance and investment problem for an insurer whose surplus process is approximated by a drifted Brownian motion. Proportional reinsurance is to hedge the risk of insurance. Interest rate risk and inflation risk are considered. We suppose that the instantaneous nominal interest rate follows an Ornstein–Uhlenbeck process, and the inflation index is given by a generalized Fisher equation. To make the market complete, zero-coupon bonds and Treasury Inflation Protected Securities (TIPS) are included in the market. The financial market consists of cash, zero-coupon bond, TIPS and stock. We employ the stochastic dynamic programming to derive the closed-forms of the optimal reinsurance and investment strategies as well as the optimal utility function under the constant relative risk aversion (CRRA) utility maximization. Sensitivity analysis is given to show the economic behavior of the optimal strategies and optimal utility.     

变折现率下带含糊厌恶与预期的最优投资研究

本文采用折现率为时间的函数下的递推多先验效用,研究Merton模型在带预期条件下的最优消费和投资组合决策问题,其中含糊与风险是有区别的.在幂效用函数情形下,刻画了投资者最优投资决策,表明了含糊厌恶和预期对最优投资的影响.最优投资组合决策由倒向随机微分方程和Malliavin导数导出.     

Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making

Natural basic concepts in multiple-objective optimization lead to difficult multiextremal global optimization problems. Examples include detection of efficient points when nonconvexities occur, and optimization of a linear function over the efficient set in the convex (even linear) case. Assuming that a utility function exists allows one to replace in general the multiple-objective program by a single, nonconvex optimization problem, which amounts to a minimization over the efficient set when the utility function is increasing. A new algorithm is discussed for this utility function program which, under natural mild conditions, converges to an -approximate global solution in a finite number of iterations. Applications include linear, convex, indefinite quadratic, Lipschitz, and d.c. objectives and constraints.     

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.     

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.     

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.     

梁线模型在半刚性连接预制综合管廊中的应用

预制综合管廊在侧壁中间设置拼缝,采用预应力筋连接,连接接头既能发生相对转动,又能传递弯矩,具有半刚性特征。梁线模型将半刚性梁的弯矩–转角直线（需求线）与接头的弯矩–转角曲线（性能线）绘制在一起,通过两者的交点可以确定接头转动刚度。采用经试验验证的Abaqus有限元模型,开展了以拼缝界面应力和壁厚为主要参数的接头受弯有限元分析。基于有限元分析结果,提出了梁线模型用于预应力筋连接预制拼装管廊的结构设计方法。

     

Social welfare relations and irregular sets

Social welfare relations satisfying Pareto and equity principles on infinite utility streams have revealed a non-constructive nature, specifically by showing that in general they imply the existence of non-Ramsey sets and non-Lebesgue measurable sets. In [4, Problem 11.14], the authors ask whether such a connection holds with non-Baire sets as well. In this paper we answer such a question showing that several versions of Pareto principles acting on different utility domains imply the existence of non-Baire sets. Furthermore, we analyze in more details the needed fragments of AC and we start a systematic investigation of a social welfare diagram in a similar fashion done in the past decades concerning cardinal invariants and regularity properties of the reals. In doing that we use tools from forcing theory, such as specific tree-forcings (in particular variants of Silver and Mathias forcings) and Shelah's amalgamation.     

需求风险下套期保值与市场进入分析

需求风险是企业面临的主要风险之一,对企业的生产经营和管理决策具有重要影响。本文考虑由多个风险厌恶企业构成的产品竞争市场,分析了需求风险下企业参与套期保值和市场进入的决策问题。文章首先通过Cournot博弈分析了套期保值对于规避需求风险的作用和意义;然后,探讨了企业参与套期保值和市场进入的决策过程,并给出了三种情形下的市场均衡结构;最后,通过数值实验对结论进行了验证。研究表明:套期保值提高了企业应对需求风险的能力,使企业获得更高的产量和收益;参与套期保值企业数量随着进入市场企业数量的增加而减少;当市场竞争程度或市场费用增加时,将会有更多的企业选择参与套期保值,而选择进入市场的企业会减少。     

Mean-Variance Hedging Under Multiple Defaults Risk

We solve a mean-variance hedging problem in an incomplete market where multiple defaults can occur. For this purpose, we use a default-density modeling approach. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the dependence of the default times is modelled using a conditional density hypothesis. We prove the quadratic form of each value process between consecutive default times and recursively solve systems of coupled quadratic backward stochastic differential equations (BSDEs). We demonstrate the existence of these solutions using BSDE techniques. Then, using a verification theorem, we prove that the solutions of each subcontrol problem are related to the solution of our global mean-variance hedging problem. As a byproduct, we obtain an explicit formula for the optimal trading strategy. Finally, we illustrate our results for certain specific cases and for a multiple defaults case in particular.