Moment-based density approximations for aggregate losses

The determination of the distribution of aggregate losses is of crucial importance for an insurer. In this paper, we propose a technique for approximating the distribution of univariate and bivariate aggregate losses, which is solely based on their moments. Accordingly, this methodology can be implemented without any specific knowledge of the claim number or size distributions. The numerical examples presented herein indicate that the proposed approach constitutes a viable alternative to the commonly used recursive and FFT methods.     

Minimizing capital injections by investment and reinsurance for a piecewise deterministic reserve process model

We consider the possibility for an insurance company to rely on capital injections to bring the reserve back to a given level if it has fallen below it and study the problem of dynamically choosing the reinsurance level and the investment in the financial market in order to minimize the expected discounted total amount of capital injection. The reserve process is described by a piecewise deterministic process, where the random discontinuities are triggered by the arrival of a claim or by a change in the prices of the risky assets in which the company invests. The capital injections, combined with the specific model, make the problem non-linear and difficult to solve via an HJB approach. The emphasis here is on making the actual computation of a solution possible by value iteration combined with an approximation based on discretization. This leads to a nearly optimal solution with an approximation that can be made arbitrarily precise. Numerical results show the feasibility of the proposed approach.     

Monitoring risk in a ruin model perturbed by diffusion

We construct a nonparametric sequential test for the ruin probability and a corresponding change-point test in a risk model perturbed by diffusion. Some limiting properties are derived, which extend and improve on recent results of Conti (Stat Prob Lett 72:333–343, 2005) and Jahnke (Diploma thesis, University of Cologne, 2007). It is shown that the monitoring procedures can be designed such that the tests have an asymptotic prescribed false alarm rate (size) α and power 1. Some results from a small simulation study are also presented.     

一种新的频率规划方法

本文针对目前频率规划中存在的问题，提出了利用专家系统和改进遗传算法及分层技术等来克服手工频率规划过于烦琐和电子地图要求极高及频带紧张的障碍，从而在缺少准确电子地图的情况下，借助专家的经验和知识同时利用改进的优化算法亦能给出较准确的频率规划方案。同时提出了改进的模糊似然推理方法。此外我们开发了智能多层频率规划ＣＡＤ软件包，并给出仿真结果。     

Determining the implied volatility for American options using the QAM

This paper describes an efficient numerical procedure which may be used to determine implied volatilities for American options using the quadratic approximation method. Simulation results are presented. The procedure usually converges in five or six iterations with extreme accuracy under a wide variety of option market conditions. A comparison of American implied volatilities with European model implied volatilities indicates that significant differences may arise. This suggests that reliance on European model volatilities estimates may lead to significant pricing errors.     

Value-at-Risk computation by Fourier inversion with explicit error bounds

The Value-at-Risk of a delta–gamma approximated derivatives portfolio can be computed by numerical integration of the characteristic function. However, while the choice of parameters in any numerical integration scheme is paramount, in practice it often relies on ad hoc procedures of trial and error. For normal and multivariate t-distributed risk factors, we show how to calculate the necessary parameters for one particular integration scheme as a function of the data (the distribution of risk factors, and delta and gamma) in order to satisfy a given error tolerance. This allows for implementation in a fully automated risk management system. We also demonstrate in simulations that the method is significantly faster than the Monte Carlo method, for a given error tolerance.     

Continuum approximation models for joint delivery systems using trucks and drones

ABSTRACT

This research focuses on exploring the economics related to the joint delivery system using trucks and drones. Transportation distances and costs are approximated as simple functions using continuum approximation (CA) methods, which can keep key issues and tradeoffs in focus. The main contribution is to develop cost models using the derived methods and gain a greater understanding of delivery activities by focusing on the tradeoffs between major components, which are valuable for decision-makers: choose economical delivery mode based on customer density, partition service region into optimal sub-regions, and obtain an optimal delivery ratio between trucks and drones.     

高炮随动系统测试中的数据处理方法

在某型高炮随动系统的测试中,待测信号有非时变信号和时变信号两种。本文根据这两种信号的特点,对比分析了一阶差分法、多项式逼近法和线性回归法,对每种方法的处理方式进行了研究,得到了以上两种信号的处理方法。     

Empirical likelihood confidence intervals for the Gini measure of income inequality

Gini coefficient is among the most popular and widely used measures of income inequality in economic studies, with various extensions and applications in finance and other related areas. This paper studies confidence intervals on the Gini coefficient for simple random samples, using normal approximation, bootstrap percentile, bootstrap-t and the empirical likelihood method. Through both theory and simulation studies it is shown that the intervals based on normal or bootstrap approximation are less satisfactory for samples of small or moderate size than the bootstrap-calibrated empirical likelihood ratio confidence intervals which perform well for all sample sizes. Results for stratified random sampling are also presented.