Approximation of Optimal Reinsurance and Dividend Payout Policies

We consider the stochastic process of the liquid assets of an insurance company assuming that the management can control this process in two ways: first, the risk exposure can be reduced by affecting reinsurance, but this decreases the premium income; and second, a dividend has to be paid out to the shareholders. The aim is to maximize the expected discounted dividend payout until the time of bankruptcy. The classical approach is to model the liquid assets or risk reserve process of the company as a piecewise deterministic Markov process. However, within this setting the control problem is very hard. Recently several papers have modeled this problem as a controlled diffusion, presuming that the policy obtained is in some sense good for the piecewise deterministic problem as well. We will clarify this statement in our paper. More precisely, we will first show that the value function of the controlled diffusion provides an asymptotic upper bound for the value functions of the piecewise deterministic problems under diffusion scaling. Finally it will be shown that the upper bound is achieved in the limit under the optimal feedback control of the diffusion problem. This property is called asymptotic optimality .     

Exercise Regions And Efficient Valuation Of American Lookback Options

This paper presents an efficient method to compute the values and early exercise boundaries of American fixed strike lookback options. The method reduces option valuation to a single optimal stopping problem for standard Brownian motion and an associated path-dependent functional, indexed by one parameter in the absence of dividends and by two parameters in the presence of a dividend rate. Numerical results obtained by this method show that, after a space-time transformation, the stopping boundaries are well approximated by certain piecewise linear functions with a few pieces, leading to fast and accurate approximations for American lookback option values. An explicit decomposition formula for American lookback options is derived and applied not only to the development of these approximations but also to the asymptotic analysis of the early exercise boundary near the expiration date.     

CVaR HEDGING USING QUANTIZATION‐BASED STOCHASTIC APPROXIMATION ALGORITHM

In this paper, we investigate a method based on risk minimization to hedge observable but nontradable source of risk on financial or energy markets. The optimal portfolio strategy is obtained by minimizing dynamically the conditional value‐at‐risk (CVaR) using three main tools: a stochastic approximation algorithm, optimal quantization, and variance reduction techniques (importance sampling and linear control variable), as the quantities of interest are naturally related to rare events. As a first step, we investigate the problem of CVaR regression, which corresponds to a static portfolio strategy where the number of units of each tradable assets is fixed at time 0 and remains unchanged till maturity. We devise a stochastic approximation algorithm and study its a.s. convergence and weak convergence rate. Then, we extend our approach to the dynamic case under the assumption that the process modeling the nontradable source of risk and financial assets prices is Markovian. Finally, we illustrate our approach by considering several portfolios in connection with energy markets.     

一种基于系统采样时钟量化的无人机测距方法

为了解决基于单载波频域均衡(SC-FDE)高速数据链无人机测控系统的地空双向距离测量问题,提出了一种基于系统采样时钟量化的无人机测距方法,将机载/地面测距信息分别量化至机/地系统采样时钟的计时器,完成地空双向距离的测量。理论分析和地空链路测试平台实验结果表明,新方法在复杂多径环境下实现了地空双向距离测量,降低了测距分系统的设计复杂度,地空双向实际测距均值与等效自由空间传输延迟一致,且测距精度满足理论测距误差设计值。该测距方法在无人机测控系统中具有良好的应用前景。     

一种基于码本轮转的有限反馈量化方法

大规模多输入多输出（Multiple-Input Multiple-Output，MIMO）系统中随着天线数目的增加，其反馈比特数将随之大幅度增加。为此，提出了一种基于码本轮转的有限反馈量化方法。该方法中，用户在前一时刻得到最佳码字之后，在码本中选取轮转区域构成虚拟码本，判断当前时刻的信道向量，满足轮转条件的用户将虚拟码本轮转到码本起始位置，在虚拟码本中进行量化；不满足轮转条件的用户在原始码本中进行量化，选出当前时刻的最优码字。反馈比特数分析与仿真结果表明，所提方法可轮转的虚拟码本减少了量化码字的数量，从而减少了反馈比特数，是系统性能与反馈比特数的一种折中。     

Optimal approximations of nonlinear payoffs in static replication

Static replication of nonlinear payoffs by line segments (or equivalently vanilla options) is an important hedging method, which unfortunately is only an approximation. If the strike prices of options are adjustable (for OTC options), two optimal approximations can be defined for replication by piecewise chords. The first is a naive minimum area approach, which seeks a set of strike prices to minimize the area enclosed by the payoff curve and the chords. The second improves on the first by taking the conditional distribution of the underlying into consideration, and minimizes the expected area instead. When the strike prices are fixed (for exchange‐traded options), a third or the approach of least expected squares locates the minimum for the expected sum of squared differences between the payoff and the replicating portfolio, by varying the weights or quantities of the options used in the replication. For a payoff of variance swap, minimum expected area and least expected squares are found to produce the best numerical results in terms of cost of replication. Finally, piecewise tangents can also be utilized in static replication, which together with replication by chords, forms a pair of lower or upper bound to a nonlinear payoff. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark     

A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS

We present here the quantization method which is well-adapted for the pricing and hedging of American options on a basket of assets. Its purpose is to compute a large number of conditional expectations by projection of the diffusion on optimal grids designed to minimize the (square mean) projection error ( Graf and Luschgy 2000 ). An algorithm to compute such grids is described. We provide results concerning the orders of the approximation with respect to the regularity of the payoff function and the global size of the grids. Numerical tests are performed in dimensions 2, 4, 5, 6, 10 with American style exchange options. They show that theoretical orders are probably pessimistic.     

使用变换域编码技术压缩SAR原始数据

首先分析了在合成孔径雷达（SAR）原始数据中通常使用的块自适应量化（BAQ）算法，然后在此基础上详细讨论了两种基于块自适应量化的变换域编码算法，即基于快速傅里叶变换块自适应量化（FFT-BAQ）和基于小波变换块自适应量化（WT-BAQ），并对这两种算法压缩得到数据解压缩获得图像与块自适应量化得到的图像进行分析比较，结果显示变换域编码技术能改善SAR原始数据压缩性能。     

采用高速DSP实现BAQ算法的应用研究

本文较为详细地介绍了最佳量化的基本方法以及块自适应量化编码的原理，同时给出了采用高速DSP芯片技术实现SAR原始数据压缩的原理和实现结果。     

Developing Group Ordered Weighted Averaging Operator Weights for Group Decision Support

A few single decision-making methods under uncertainty (SDMUU) are available in the literature. The reason for such scarcity seems to be mainly due to too insufficient information to induce a reasonable result for effective decision support. Moreover their final outcomes on the same SDMUU problem may be different depending on which method is applied. A group decision-making method under uncertainty (GDMUU) extends a SDMUU in a sense that a group of individuals, each expressing different opinions, work together to solve a relevant problem. As in a SDMUU, we find that just a few methods are available to solve a GDMUU problem. In the paper, the ordered weighted averaging (OWA) method, originally devised for use with the SDMUU problem, is considered to deal with a GDMUU problem where individuals of a group express their degree of optimism in terms of attitudinal characters. We first find the extreme points corresponding to the attitudinal character and then solve a quadratic mathematical program which minimizes a squared distance from each extreme point identified. Thus the resulting OWA operator weights for the group are located at the center of the weights-space constructed by attitudinal characters. This idea is further extended to deal with uncertain attitudinal character expressed in the form of interval in situations where it is difficult to reliably obtain a precise attitudinal character due to time pressure and a limited domain knowledge and so on.     

An application of finite elements to option pricing

This study applied the finite element method (FEM) to pricing options. The FEM estimates the function that satisfies a governing differential equation through the assembly of piecewise continuous functions over the domain of the problem. Two common representations, a variational functional representation, and a weighted residual representation are used in the application of the method. The FEM is a versatile alternative to other popular lattice methods used in option pricing. Advantages include the abilities to directly estimate the Greeks of the option and allow nonuniform mesh construction. As an illustration of the advantages that the FEM offers, the method was used to price European put options and discrete barrier knock‐out put options. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:19–42, 2001     

基于矩量法对一种手机天线的特性分析

本文基于矩量法，对一种便携式手机天线的特性进行了研究，利用Pocklington积分方程和Galerkin法，采用分域基函数展开模式，得出了矩形导电机壳及单极天线上的电流分布和输入阻抗，并对几种不同尺寸导电机壳上的天线特性进行了分析。计算结果表明导电机壳尺寸在很大程度上影响天线的性能，合理选择导电机壳尺寸可有效调节便携式手机天线的性能。     

Turbo码在无线图像传输系统中的应用

通过Matlab仿真,信源编码采用矢量量化法,对静止图像通过无线瑞利(Rayleigh)衰落信道传输时,不采用信道编码和采用Turbo码作为信道编码两种情况进行了研究。依据失真度的主观评价,对两种情况下重构的图像进行了比较和分析。结果表明,Turbo码具有很强的抗衰落和抗多径效应能力,它不仅有效地提高了无线图像传输的可靠性,而且大大节省了系统发射功率。     

A support vector machine (SVM) approach to imbalanced datasets of customer responses: comparison with other customer response models

Customer response is a crucial aspect of service business. The ability to accurately predict which customer profiles are productive has proven invaluable in customer relationship management. An area that has received little attention in the literature on direct marketing is the class imbalance problem (the very low response rate). We propose a customer response predictive model approach combining recency, frequency, and monetary variables and support vector machine analysis. We have identified three sets of direct marketing data with a different degree of class imbalance (little, moderate, high) and used random undersampling method to reduce the degree of the imbalance problem. We report the empirical results in terms of gain values and prediction accuracy and the impact of random undersampling on customer response model performance. We also discuss these empirical results with the findings of previous studies and the implications for industry practice and future research.     

MPEG-4 AAC音频编码中量化模块的改进

MPEG-4 AAC音频编码标准中的量化过程采用了Brandenburg提出的双循环模式,取得 了较好的编码质量和压缩比例。但在实际编码时,该方法由于迭代次数过多,会出现收敛速 度较慢,甚至死锁的情况。在深入分析MPEG-4 AAC量化算法的基础上,提出了一种快速 计算每个比例因子频带的改进算法。该算法通过有效减少外循环计算过程,并确保每个比例 因子频带的量化失真低于允许值,从而减少量化模块的计算量。实验结果表明,在不影响音 频编码质量的前提下,该算法能有效地提高编码效率。     

Assigning television commercial videotapes to time slots under alternative message spacing policies

A number of studies in the psychological and marketing literature have focused on the effects of message spacing on consumer memory and judgement. The importance of message spacing has also been exemplified by a crucial scheduling problem in the broadcast television industry that requires the assignment of multiple airings of commercial videotapes to purchased slots of air time. Existing models for this problem are restricted to the case of equal spacing of successive airings in terms of slot position. In light of the fact that equal spacing of messages is not necessarily the best course of action in all situations, we present an alternative model that enables greater flexibility with respect to the spacing of commercial messages. For example, the model allows for equal temporal spacing of commercials in addition to equal spacing in terms of slot position. More importantly, the model permits spacing options that allow for pulsing strategies associated with well-separated bursts of commercial airings, as well as the consideration of spacing decisions when commercials have different durations. We demonstrate a heuristic for solving the scheduling problem under various message spacing policies. We believe that our model, which is effective and adaptable, has considerable promise for practical scheduling problems as well as subsequent experimental research.     

基于自适应分割算法的多跳频信号盲检测

传统的观点大都将跳频信号盲检测问题视为能量域的门限阈值问题,而从统计域来看,实际接收到的跳频信号是在一些未知时刻突变而在这些时刻之间保持统计平稳性的分段平稳随机信号,那么基于非平稳时间序列的各种突变检测算法就可以引入其中。分析了当前跳频突变通信信号的统计特性,给出了其高阶分段平稳的模型。将Bemaola-Galan（BG）提出的自适应分割算法推导到高阶,并将其成功应用于多个跳频突发信号盲检测和自适应提取中。仿真结果表明,该算法不需要任何先验信息,能够有效检测和提取多个突发通信信号,且性能优于传统的能量检测法。     

Option Pricing For Jump Diffusions: Approximations and Their Interpretation

We derive a computable approximation for the value of a European call option when prices satisfy a jump-diffusion model with the coefficients depending explicitly on time. This is achieved by approximating the original coefficients with functions that are piecewise constant in time. We give an interpretation of the approximating option values, in particular in the context of a discrete-time model associated with the approximating continuous-time model.     

ADC量化位数对阵列天线GNSS接收机的影响

在处理全球卫星导航系统（Global Navigation Satellite System,GNSS）卫星信号时,针对模数转换器（Analog-to-Digital Converter,ADC）量化位数不同导致输出的信号信噪比下降的问题,推导了阵列天线波束形成后输出信号的信噪比理论计算模型,分析了ADC量化位数对阵列天线抗干扰GNSS接收机的性能影响。在7阵元天线且ADC量化位数为10的条件下,理论模型分析和数据仿真结果表明最大抗干扰能力约为85 dB。通过确定ADC量化位数与抗干扰GNSS接收机抗干扰能力之间的关系,其结论为工程应用中抗干扰GNSS接收机的ADC选型和设计提供了理论依据。     

A FIRST‐ORDER BSPDE FOR SWING OPTION PRICING: CLASSICAL SOLUTIONS

In a companion paper, we studied a control problem related to swing option pricing in a general non‐Markovian setting. The main result there shows that the value process of this control problem can uniquely be characterized in terms of a first‐order backward stochastic partial differential equation (BSPDE) and a pathwise differential inclusion. In this paper, we additionally assume that the cash flow process of the swing option is left‐continuous in expectation. Under this assumption, we show that the value process is continuously differentiable in the space variable that represents the volume in which the holder of the option can still exercise until maturity. This gives rise to an existence and uniqueness result for the corresponding BSPDE in a classical sense. We also explicitly represent the space derivative of the value process in terms of a nonstandard optimal stopping problem over a subset of predictable stopping times. This representation can be applied to derive a dual minimization problem in terms of martingales.