三类索赔额分布下的破产概率的模拟值及其R实现

破产概率的计算是精算破产理论的经典问题,对当前保险经营风险的度量有重要的理论意义和参考价值。在以往对破产概率的研究中,出于理论分析的方便,往往假设索赔额分布具有特殊的形式,而对更复杂的索赔额分布,求出理论上的解析解往往是不可行的,为此需要求解数值解。随机模拟是很重要的一种求数值解的方法。本文考虑三类索赔额分布:伽玛分布、对数正态分布、逆高斯分布,对每类分布,通过模拟不同参数下的索赔额,得到破产频数、首次破产对应的索赔次数的期望及标准差,并运用R软件对不同索赔额分布下的模拟结果进行比较分析。     

Continuous‐time mean–variance portfolio selection: A reinforcement learning framework

We approach the continuous‐time mean–variance portfolio selection with reinforcement learning (RL). The problem is to achieve the best trade‐off between exploration and exploitation, and is formulated as an entropy‐regularized, relaxed stochastic control problem. We prove that the optimal feedback policy for this problem must be Gaussian, with time‐decaying variance. We then prove a policy improvement theorem, based on which we devise an implementable RL algorithm. We find that our algorithm and its variant outperform both traditional and deep neural network based algorithms in our simulation and empirical studies.     

Marginal consistent dependence modelling using weak subordination for Brownian motions

We present an approach for modelling dependencies in exponential Lévy market models with arbitrary margins originated from time changed Brownian motions. Using weak subordination of Buchmann et al. [Bernoulli, 2017], we face a new layer of dependencies, superior to traditional approaches based on pathwise subordination, since weakly subordinated processes are not required to have independent components considering multivariate stochastic time changes. We apply a subordinator being able to incorporate any joint or idiosyncratic information arrivals. We emphasize multivariate variance gamma and normal inverse Gaussian processes and state explicit formulae for the Lévy characteristics. Using maximum likelihood, we estimate multivariate variance gamma models on various market data and show that these models are highly preferable to traditional approaches. Consistent values of basket-options under given marginal pricing models are achieved using the Esscher transform, generating a non-flat implied correlation surface.     

PRICING SWAPTIONS UNDER MULTIFACTOR GAUSSIAN HJM MODELS

Several approximations have been proposed in the literature for the pricing of European‐style swaptions under multifactor term structure models. However, none of them provides an estimate for the inherent approximation error. Until now, only the Edgeworth expansion technique of Collin‐Dufresne and Goldstein is able to characterize the order of the approximation error. Under a multifactor HJM Gaussian framework, this paper proposes a new approximation for European‐style swaptions, which is able to set bounds on the magnitude of the approximation error and is based on the conditioning approach initiated by Curran and Rogers and Shi. All the proposed pricing bounds will arise as a simple by‐product of the Nielsen and Sandmann setup, and will be shown to provide a better accuracy–efficiency trade‐off than all the approximations already proposed in the literature.     

铁路运输危险气体泄漏扩散模拟分析

针对铁路运输危险气体泄漏事故的特点,文章以高斯烟羽模型为基础,借助Matlab编程对不同条件下(不同风速、不同大气稳定条件和多泄漏源等)的铁路危险性气体扩散范围进行模拟分析,实现了危险性气体扩散的直观图形表示和伤害分区的划分,为指导铁路运输紧急救援提供一定的指导作用。     

数值保角变换的新算法

保角变换理论在流体力学等许多领域中有着广泛的应用。但计算保角变换是个很困难的问题,因此寻求一种有效方法计算保角变换在实际应用中具有很大意义。本论文提出了一种数值保角变换的新算法,在这个新算法中我们在改进高斯消去法的基础上利用模拟电荷法计算新的电荷点,进而构造高精度的近似保角变换函数,并且通过典型图形的数值实验检验了新算法的有效性。     

一种用于UWB系统的高斯脉冲发生器

提出了一种新型的用于超宽带系统的高斯脉冲发生器.该脉冲发生器采用阶跃恢复二极管,结构简单,且易于实现.电路中加入一个放大器,以便阻止反射波对阶跃恢复二极管的影响,较好地抑制了脉冲尾部的波动,并使用共面波导实现.该极窄高斯脉冲的脉宽仅为300ps,且有很好的对称性.     

一种改进的图像压缩感知稀疏恢复算法

稀疏信号的分布模型是影响基于近似信息传递（AMP）的压缩感知(CS)信号重建效果的关键因素。因实际图像的小波近似系数、各级的水平细节系数、垂直细节系数以及对角细节系数的模型参数存在较大差异,现有基于拉普拉斯、贝努力高斯(BG)和高斯混合等模型的AMP方法因未考虑此差异而影响重建效果。为了提高模型估计的准确性,将各级小波系数的BG模型参数分开估计,进而提出了一种改进的图像压缩感知稀疏重建的新方法,即期望最大分段贝努力高斯近似信息传递算法（EM-SSBG-AMP）。仿真结果表明,相同采样率下,新算法的峰值信噪比（PSNR）明显高于5阶期望最大高斯混合近似信息传递算法(EM-GM-AMP),重建时间与5阶EM-GM-AMP相当。     

基于GPR模型的中国“十三五”时期碳排放趋势预测

系统分析了中国CO2排放的影响因素,在此基础上建立了基于高斯过程回归的CO2排放预测模型,运用历史数据进行模型精度检验,并与传统的GM(1,1)模型、人工神经网络和支持向量机的预测结果比较。结合情景设计,预测了中国"十三五"时期的CO2排放量和CO2排放强度。结果表明:高斯过程回归模型具有显著的精度优势,中国能达到2020年CO2排放强度较2005年下降40%~45%的减排目标。指出:对于CO2减排,应结合各地区的实际情况灵活处理,以调整产业结构、优化能源结构、推动技术创新为重点,不可片面牺牲经济发展。     

Estimating stochastic volatility models using integrated nested Laplace approximations

Volatility in financial time series is mainly analysed through two classes of models; the generalized autoregressive conditional heteroscedasticity (GARCH) models and the stochastic volatility (SV) ones. GARCH models are straightforward to estimate using maximum-likelihood techniques, while SV models require more complex inferential and computational tools, such as Markov Chain Monte Carlo (MCMC). Hence, although provided with a series of theoretical advantages, SV models are in practice much less popular than GARCH ones. In this paper, we solve the problem of inference for some SV models by applying a new inferential tool, integrated nested Laplace approximations (INLAs). INLA substitutes MCMC simulations with accurate deterministic approximations, making a full Bayesian analysis of many kinds of SV models extremely fast and accurate. Our hope is that the use of INLA will help SV models to become more appealing to the financial industry, where, due to their complexity, they are rarely used in practice.