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.     

Gaussian risk models with financial constraints

In this paper, we investigate Gaussian risk models which include financial elements, such as inflation and interest rates. For some general models for inflation and interest rates, we obtain an asymptotic expansion of the finite-time ruin probability for Gaussian risk models. Furthermore, we derive an approximation of the conditional ruin time by an exponential random variable as the initial capital tends to infinity.     

GUARANTEED MINIMUM WITHDRAWAL BENEFIT IN VARIABLE ANNUITIES

We develop a singular stochastic control model for pricing variable annuities with the guaranteed minimum withdrawal benefit. This benefit promises to return the entire initial investment, with withdrawals spread over the term of the contract, irrespective of the market performance of the underlying asset portfolio. A contractual withdrawal rate is set and no penalty is imposed when the policyholder chooses to withdraw at or below this rate. Subject to a penalty fee, the policyholder is allowed to withdraw at a rate higher than the contractual withdrawal rate or surrender the policy instantaneously. We explore the optimal withdrawal strategy adopted by the rational policyholder that maximizes the expected discounted value of the cash flows generated from holding this variable annuity policy. An efficient finite difference algorithm using the penalty approximation approach is proposed for solving the singular stochastic control model. Optimal withdrawal policies of the holders of the variable annuities with the guaranteed minimum withdrawal benefit are explored. We also construct discrete pricing formulation that models withdrawals on discrete dates. Our numerical tests show that the solution values from the discrete model converge to those of the continuous model.     

Traditional versus non-traditional reinsurance in a dynamic setting

We consider a stochastic risk reserve process whose risk exposure can be controlled dynamically by applying proportional reinsurance and by issuing CAT Bonds. The CAT Bond payments are only partly correlated with the insurers losses. The aim is to minimize the probability of ruin. Using a two-dimensional diffusion approximation we obtain a controlled diffusion problem which can be solved explicitly with the help of the HJB equation. We present some numerical results and discuss to which extend the proportional reinsurance can be replaced by issuing CAT Bonds.     

H＋与B原子碰撞电离微分散射截面的研究

利用初态程函近似一连续扭曲波方法（CDW—EIS）研究了质子与B原子的碰撞电离过程。计算了入射粒子能量分别为100keV／u,1000keV／u,10000keV／u情况下的1s、2s、2p分波电离二阶微分截面及其总的二阶微分散射截面。并利用计算结果详细讨论和分析了软碰撞（SC）、电子俘获到入射粒子连续态（ECC）和两体相遇碰撞（BE）的碰撞电离机理,并对各分波二阶微分散射截面进行了比较。     

An outer approximation algorithm for the robust shortest path problem

This paper describes a new algorithm for the stochastic shortest path problem where path costs are a weighted sum of expected cost and cost standard deviation. We allow correlation between link costs, subject to a regularity condition excluding unbounded solutions. The chief complication in this variant is that path costs are not an additive sum of link costs. In this paper, we reformulate this problem as a conic quadratic program, and develop an outer-approximation algorithm based on this formulation. Numerical experiments show that the outer-approximation algorithm significantly outperforms standard integer programming algorithms implemented in solvers.     

Portfolio Value-at-Risk with Heavy-Tailed Risk Factors

This paper develops efficient methods for computing portfolio value-at-risk (VAR) when the underlying risk factors have a heavy-tailed distribution. In modeling heavy tails, we focus on multivariate t distributions and some extensions thereof. We develop two methods for VAR calculation that exploit a quadratic approximation to the portfolio loss, such as the delta-gamma approximation. In the first method, we derive the characteristic function of the quadratic approximation and then use numerical transform inversion to approximate the portfolio loss distribution. Because the quadratic approximation may not always yield accurate VAR estimates, we also develop a low variance Monte Carlo method. This method uses the quadratic approximation to guide the selection of an effective importance sampling distribution that samples risk factors so that large losses occur more often. Variance is further reduced by combining the importance sampling with stratified sampling. Numerical results on a variety of test portfolios indicate that large variance reductions are typically obtained. Both methods developed in this paper overcome difficulties associated with VAR calculation with heavy-tailed risk factors. The Monte Carlo method also extends to the problem of estimating the conditional excess, sometimes known as the conditional VAR.