Optimal dynamic reinsurance with dependent risks: variance premium principle

In this paper, we consider the optimal proportional reinsurance strategy in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. Under the criterion of maximizing the expected exponential utility with the variance premium principle, we adopt a nonstandard approach to examining the existence and uniqueness of the optimal reinsurance strategy. Using the technique of stochastic control theory, closed-form expressions for the optimal strategy and the value function are derived for the compound Poisson risk model as well as for the Brownian motion risk model. From the numerical examples, we see that the optimal results for the compound Poisson risk model are very different from those for the diffusion model. The former depends not only on the safety loading, time, and the interest rate, but also on the claim size distributions and the claim number processes, while the latter depends only on the safety loading, time, and the interest rate.     

Optimal investment-consumption-insurance with random parameters

This paper discusses an optimal investment, consumption, and life insurance purchase problem for a wage earner in a complete market with Brownian information. Specifically, we assume that the parameters governing the market model and the wage earner, including the interest rate, appreciation rate, volatility, force of mortality, premium-insurance ratio, income and discount rate, are all random processes adapted to the Brownian motion filtration. Our modeling framework is very general, which allows these random parameters to be unbounded, non-Markovian functionals of the underlying Brownian motion. Suppose that the wage earner’s preference is described by a power utility. The wage earner’s problem is then to choose an optimal investment-consumption-insurance strategy so as to maximize the expected, discounted utilities from intertemporal consumption, legacy and terminal wealth over an uncertain lifetime horizon. We use a novel approach, which combines the Hamilton–Jacobi–Bellman equation and backward stochastic differential equation (BSDE) to solve this problem. In general, we give explicit expressions for the optimal investment-consumption-insurance strategy and the value function in terms of the solutions to two BSDEs. To illustrate our results, we provide closed-form solutions to the problem with stochastic income, stochastic mortality, and stochastic appreciation rate, respectively.     

随机数在随机事件与概率教学中的应用探索

本文对在随机事件与概率中的常见问题提出了一种新的借助于计算机实现的解决思路,即通过机器自动产生随机数后构建相应的数学模型,再通过编程计算得到最后结果。该方法既为概率论的教学带来了创新性思维,也为当前的教师提出了新的挑战。     

On sustained economic growth with wealth effects

In a discounted one-sector convex model of optimal economic growth where utility may depend on both consumption and capital stock, I derive necessary and sufficient conditions for sustained growth (unbounded expansion of capital and consumption). Conditions for bounded growth and extinction are also outlined. Optimal paths may be non-monotone. Sustained growth may occur even though the asymptotic marginal productivity is less than the discount rate and may require the initial capital stock to be above a critical level. The behavior of the marginal rate of substitution between consumption and capital plays a crucial role in the conditions.     

考虑BI保险的供应链中断模型分析

突发事件引起的供应链中断,会造成供应链成员巨大的经济损失。以一个二级供应链为基础,考虑存在供应中断风险情况下,引入BI保险,建立供应中断下制造商不投保、制造商单独投保、以及制造商和零售商联合投保模型,探究零售商和制造商利润、最优订购量、最优批发价等参数的变化趋势,其理论分析结果为决策部门提供指导。     

Securities Transaction Tax and Market Efficiency: Evidence from the Japanese Experience

This study examines the effect of transaction costs on the time series behavior of stock returns over a period surrounding the April 1989 changes in tax rates on securities transactions and capital gains in Japan. We find significant decreases in estimates of the first-order autocorrelation in returns for Japanese stocks listed in Japan, but no changes for Japanese stocks dually listed in the United States as American Depository Receipts (ADRs), which were not subject to the tax law change. We also find lower price basis between the ADRs and their underlying Japanese stocks. These results are consistent with the hypothesis that a reduction in transaction costs improves the efficiency of the price discovery process.

$$\mathcal{D}$$-optimal Minimum Support Mixture Designs in Blocks

An easy method to construct efficient blocked mixture experiments in the presence of fixed and/or random blocks is presented. The method can be used when qualitative variables are involved in a mixture experiment as well. The resulting designs are -optimal in the class of minimum support designs. It is illustrated that the minimum support designs are more efficient than orthogonally blocked mixture experiments presented in the literature and only slightly less efficient than -optimal designs.     

应急物资公路运输路径优化模型的建立及求解

对应急物资运输时效性和可靠性两方面因素进行了数学描述,在分别对两个指标进行了无量纲化处理后建立了线性加权和效用函数模型,在具体算例中又将效用函数变形为关于λ的线性函数,最后通过坐标系作图将分析结果更直观地表达出来,以供应急物资调度人员根据其具体情况要求更方便快捷地选择应急物资公路运输的最优路径。     

寻找理性经济行为的逻辑新起点——试论中国传统伦理下的中庸理性经济人

在主流经济学的视野中,追求效用最大化是社会个体理性行为的基本准则。文章认为主流经济学理性假设的根本问题在于没有揭示特定人类社会的独特复杂特征。主流经济学家忽略了在现实生活中存在于西方文明之外的实然——中庸理性。文章尝试在以中庸理性为假设的理性经济人模型基础上,探讨中国传统伦理下中庸理性经济人的演化及其存在的可能空间。