Performance Analysis with Truncated Heavy-Tailed Distributions

This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form U ∧ K for some r.v. U with distribution B which is heavy-tailed, say Pareto or Weibull, and a typically large K, say much larger than . We study the compound Poisson ruin probability ψ(u) or, equivalently, the tail of the M/G/1 steady-state waiting time W. In the first part of the paper, we present numerical values of ψ(u) for different values of K by using the classical Siegmund algorithm as well as a more recent algorithm designed for heavy-tailed claims/service times, and compare the results to different approximations of ψ(u) in order to figure out the threshold between the light-tailed regime and the heavy-tailed regime. In the second part, we investigate the asymptotics as K → ∞ of the asymptotic exponential decay rate γ = γ ^(K) in a more general truncated Lévy process setting, and give a discussion of some of the implications for the approximations. AMS 2000 Subject Classification Primary 68M20, Secondary 60K25 †Partially supported by MaPhySto—A Network in Mathematical Physics and Stochastics, founded by the Danish National Research Foundation. An erratum to this article is available at .     

Variations in economic quality of life indicators in the U.S.A.: An interstate observation over time

Economic quality of life indices are constructed by the standardized additive method and the weighted factor loading method using more than 20 variables in each of 5 components. The resulting values are given for 1960, 1970, 1978 for all 50 states.     

利用Weibull分布对飞机某部件的金属材料的疲劳寿命的可靠性估计

本文在Ｗｅｉｂｕｌ分布下对飞机的某关键部件的金属材料的疲劳寿命进行可靠性估计，并给出了部分可靠度和可靠寿命的估计结果．     

影响高功率脉冲氙灯寿命的因素

以美国NOVA和国家点火装置用的高功率脉冲氙灯为例,结合对神光Ⅲ装置用脉冲氙灯的分析,发现了影响脉冲氙灯失效的几个因素,包括石英灯管应力、氙灯尺寸、灯管微缺陷、电极溅射、灯头绝缘、氙气纯度、封接可靠性及周围氙灯放电。结果发现:在进灯能量相同的情况下,氙灯电极弧长越长,内径越大,寿命越高;石英灯管表面的静态拉应力、内表面的微缺陷以及周围氙灯的电离辐射使得氙灯的额外负载能量大大增加,这些是导致氙灯爆炸概率变大的直接因素。     

Blow-up of solutions for a system of nonlocal singular viscoelastic equations

The main propose of this paper is to study the blow-up of solutions of an initial boundary value problem with a nonlocal boundary condition for a system of nonlinear singular viscoelastic equations. where the blow-up of solutions in finite time with nonpositive initial energy combined with a positive initial energy are shown.     

Equilibrium in natural catastrophe insurance market under disaster-resistant technologies,financial innovations and government interventions

Natural disasters increase in number and severity. Studies have shown the failure of the catastrophe insurance market by listing many causes or through developing economic models (Charpentier and Le Maux, 2014; Kousky and Cooke, 2012; Ibragimov et al., 2009). However, they have not considered the effect of the following factors on market equilibrium: advanced disaster-resistant technologies used by insureds, alternative financial innovations employed by insurers, and various disaster policies that are implemented by governments. To fill this gap, this study examines how these three factors affect the market equilibrium by changing the supply of, and demand for insurance and determines which factor(s) contributes to the market equilibrium. Furthermore, we derive the formula of position size which gives criteria for selecting index-based contracts. Overall annual numbers and insured losses of catastrophes are collected by peril type and by occurrence region listed in Sigma, which is issued by Swiss Re annually. The comparative static equilibrium analysis demonstrates that the improvement of market equilibrium is significant at low level of loss correlation in all cases. The empirical findings give insurers good references for business and geographical diversification in portfolio of catastrophe insurance policies.     

Optimal insurance with belief heterogeneity and incentive compatibility

People may evaluate risk differently in the insurance market. Motivated by this, we examine an optimal insurance problem allowing the insured and the insurer to have heterogeneous beliefs about loss distribution. To reduce ex post moral hazard, we follow Huberman et al. (1983) to assume that alternative insurance contracts satisfy the principle of indemnity and the incentive-compatible constraint. Under the assumption that the insurance premium is calculated by the expected value principle, we establish a necessary and sufficient condition for an optimal insurance solution and provide a practical scheme to improve any suboptimal insurance strategy under an arbitrary form of belief heterogeneity. By virtue of this condition, we explore qualitative properties of optimal solutions, and derive optimal insurance contracts explicitly for some interesting forms of belief heterogeneity. As a byproduct of this investigation, we find that Theorem 3.6 of Young (1999) is not completely true.     

Optimal consumption–investment and life-insurance purchase strategy for couples with correlated lifetimes

This paper presents a technique to solve the problem where a couple aims to optimize their consumption, investment, and life-insurance purchasing strategies, thereby maximizing their family objective until retirement. Assumed correlated lifetimes of the two wage earners are modeled by using both the copula and common-shock models. Subsequently, closed-form solutions are obtained for determination of the optimal strategies in both the copula and a special case of the common-shock models. As observed, use of the copula model is more advantageous in its provision of closed-form strategies and ability to distinguish mortality impacts. The optimization problem considered herein is investigated under a Markovian setting and solved using the Hamilton–Jacobi–Bellman equation. Numerical examples are also provided to illustrate the utility of the proposed optimization strategy.     

论保险投资新政对寿险公司投资收益的影响

近年来,保险监管部门颁布了多项保险投资新政,保险资金运用上的限制得到了放松.保险投资新政的实施对寿险公司投资收益有着怎样的影响呢?运用双重差分模型(DID模型),定量估计了保险投资新政实施前后的寿险公司投资收益的具体变化,并分析了何种因素对寿险公司的投资收益有显著影响.研究发现,保险投资新政对寿险公司的总投资收益率的提高有着积极的影响,保险投资新政对不同规模的寿险公司投资收益的影响存在着差异,仅考虑政策的调整因素,大型寿险公司的总投资收益率增量超过中小型寿险公司1.13%,综合考虑其它指标的影响后,其总投资收益率增量仍然超过中小型寿险公司0.097%.实证结果为保险监管部门的政策实施以及寿险公司的经营提供了新思路.     

产业生命周期视角下的并购期权价值评估方法优化研究

由于并购活动具有期权的特点,其价值常采用Black-Scholes模型计算。但传统的Black-Scholes模型没有考虑产业生命周期对并购期权价值的影响。本文分析了产业生命周期不同阶段并购期权价值的特点,指出期权价值随产业生命周期的不同发展阶段而变化。研究通过采用Gompertz曲线预测模型拟合产业生命周期曲线,并对其作适当变换,推导出了修正系数η_t,对并购期权价值的Black-Scholes评估模型进行了优化。这种优化有助于避免评估过程中的高估风险,从而使并购价值的计算更合理,确保并购决策更具科学性。