Smoothing the payoff for efficient computation of Basket option prices

We consider the problem of pricing basket options in a multivariate Black–Scholes or Variance-Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high-dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse-grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster than Monte Carlo or Quasi Monte Carlo methods in dimensions up to 35.     

拉格朗日插值多项式于平方收敛意义下的收敛逼近阶

本文得到了以 Legendre 多项式及以 Tchebycheff 多项式的导数的零点为插值结点组的拉格朗日插值多项式于平方收敛意义下的收敛速度。     

中国市场利率期限结构的静态估计

利率期限结构是资产定价、金融产品设计、保值和风险管理、套利以及投资等的基础。因此 ,对利率期限结构的估计是金融工程领域一个十分基础的工作。本文则是在这方面进行的一个尝试性研究工作。对利率期限结构的估计可以有许多方法 ,其中包括息票剥离法(bootstrapmethod)和样条估计法(splineapproximation)。本文则同时利用这两种方法对中国2001-2002的利率期限结构进行一个静态的估计 ,比较两种估计方法的静态估计结果并在此基础上分析中国利率期限结构的变化特征     

A comparison of diffusion approximations and actual limits in birth and death processes of noisy evolution

The stationary distribution of a birth and death process may not be approximated by a diffusion. The general situation is illustrated on the “musical chairs” model by Binmore et al. (1995). This model is shown to generate outcomes which are not captured by the concept of the ultralong run equilibrium selection introduced in Binmore et al. (1995).     

How accurate is the integrated vendor–buyer continuous model?

The classic single-item, deterministic-demand, integrated vendor–buyer model is revisited. The decision problem may also be viewed as that of one centralized firm, dealing with a two-level EOQ-like supply chain with finite production rates. It is sought to optimize the production lot-size and the integral number of its shipments, in equal batches, from the vendor to the buyer. While the problem calls for discrete optimization techniques, we introduced a continuous model where one can take derivatives with respect to both variables. In this short paper, we establish a 98.5% lower bound on the accuracy of this continuous model.     

A new test for analysing hysteresis in European unemployment

This article proposes a new unit root test to analyse unemployment hysteresis. The test is able to incorporate cross-sectional dependence, unattended nonlinearity and unknown structural breaks in the time-series data. This study used data on unemployment in five European countries. The findings indicated that conventional unit root tests failed to reject the null hypothesis of hysteresis for all countries. However, the newly proposed unit root test was able to reject the null hypothesis for the Spanish unemployment rate.     

PORTFOLIO SELECTION WITH MONOTONE MEAN-VARIANCE PREFERENCES

We propose a portfolio selection model based on a class of monotone preferences that coincide with mean-variance preferences on their domain of monotonicity, but differ where mean-variance preferences fail to be monotone and are therefore not economically meaningful. The functional associated with this new class of preferences is the best approximation of the mean-variance functional among those which are monotonic. We solve the portfolio selection problem and we derive a monotone version of the capital asset pricing model (CAPM), which has two main features: (i) it is, unlike the standard CAPM model, arbitrage free, (ii) it has empirically testable CAPM-like relations. The monotone CAPM has thus a sounder theoretical foundation than the standard CAPM and a comparable empirical tractability.     

基于卷积神经网络的宠物猫品种分类研究

为了提高宠物猫品种分类的准确率,提出了一种卷积神经网络融合的方法进行特征提取。首先,基于堆叠卷积自动编码器的域自适应技术,采用反卷积操作丰富特征图;其次,利用Inception结构增加网络的宽度来提取多尺度信息的特征图;最后,使用Softmox函数对图像进行分类,在Oxford-ⅢT数据集中进行实验分析。实验结果表明,利用改进后的模型对宠物猫进行分类,准确率高于对比模型,达到了84.56%,损失值为0.015 0。所提出的卷积神经网络融合方法不仅能通过丰富特征图、加深网络深度更好地表达特征,还能提高分类性能和收敛性能,较好地解决了宠物品种识别中由宠物相似所带来的识别率低的问题,还可以推广应用到其他图像相似问题的应用场景中。     

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.     

A hybrid decomposition algorithm for designing a multi-modal transportation network under biomass supply uncertainty

This study presents a two-stage stochastic programming model for the design and management of a biomass co-firing supply chain network under feedstock supply uncertainty. To represent a more realistic case, we generate scenarios from prediction errors of the historical and forecasted biomass supply availabilities. We solve the model using a hybrid decomposition algorithm that combines Sample average approximation with an enhanced Progressive hedging algorithm. The proposed algorithm is validated via a real-world case study using data from Mississippi and Alabama. Computational results indicate that the proposed algorithm is capable of producing high quality solutions in a reasonable amount of time.