基于双向长短期记忆网络的太赫兹光谱识别

特征提取是太赫兹光谱识别的关键处理步骤,通常利用降维方法作为特征提取手段。然而,当一些化合物的太赫兹光谱曲线整体差异度较小时,降维方法往往会缺失样本差异的重要特征信息,从而导致分类错误。如果不采用降维方法提取特征,传统机器学习分类算法对维数较高的原始太赫兹光谱数据又不能很好的分类。针对此问题,提出了一种基于双向长短期记忆网络（BLSTM-RNN）自动提取太赫兹光谱特征的识别方法。BLSTM-RNN作为一种特殊的循环神经网络,利用其LSTM单元可以有效解决原始太赫兹光谱数据维数较高使得模型难以训练问题。再结合模型的双向频谱信息利用架构模式,可以增强模型对复杂光谱数据自动提取有效特征信息的能力。采用三类、15种化合物太赫兹透射光谱作为测试对象,首先利用S-G滤波和三次样条插值对Anthraquinone,Benomyl和Carbazole等十五种化合物在0.9～6 THz内的太赫兹透射光谱数据进行归一化处理,然后通过构建一个具有双向长短期记忆的循环神经网络对太赫兹光谱的全频谱信息进行自动特征提取并利用Softmax分类器进行分类。通过试验优化网络结构和各项参数,最终获得了针对复杂太赫兹透射光谱数据的预测模型,并与传统机器学习算法SVM,KNN及神经网络算法MLP,CNN进行对比实验。结果表明,dataset-1和dataset-2分别作为差异度较大和无明显峰值特征的五种化合物太赫兹透射光谱数据集,其平均识别率分别为100%和98.51%,与其他方法相比识别率有所提高;最重要的是,dataset-3作为5种化合物谱线极为相似的太赫兹透射光谱数据集,其平均识别率为96.56%,与其他方法相比识别率提高显著;dataset-4作为dataset-1,dataset-2和dataset-3的透射光谱数据集集合,其平均识别率为98.87%。从而验证了BLSTM-RNN模型能自动提取有效的太赫兹光谱特征,同时又能保证复杂太赫兹光谱的预测精度。在选择模型训练优化算法方面,使用Adam优化算法要好于RMSProp,SGD和AdaGrad,其模型的目标函数损失值收敛速度最快。同时随着模型训练迭代次数增加,相似太赫兹透射光谱数据集的预测准确率也不断提升。可为复杂太赫兹光谱数据库的光谱识别检索提供一种新的识别方法。     

购买价格递减的在线租赁问题策略设计

运用在线问题与竞争分析的方法研究了购买价格递减的在线租赁问题。通过揭示相关费用函数的性质,先后给出了最优离线策略以及在线策略。通过竞争比分析,证明了我们给出的在线策略是该问题唯一最优策略,而且该策略的竞争比随购买价格的优惠率的增加呈严格递减趋势。竞争分析结果表明考虑购买价格递减因素能够改进在线策略的竞争比从而提高决策效率。     

基于投资者情绪的市场均衡分析

在行为金融研究框架下,通过分析情绪投资者与理性投资者的市场均衡条件,构建基于投资者情绪的资产定价模型,并对模型进行了数值模拟。结果表明,投资者情绪是影响资产价格的重要因素:被情绪投资者高估的资产,其回报将下降;被情绪投资者低估的资产,其回报将增加;资产回报的变化程度与情绪投资者卖出低估资产的份额正相关,与资产预期回报金额的相关系数负相关;并且,乐观情绪与悲观情绪对资产价格的作用是非对称的。     

The impact of customer returns on pricing and order decisions

In this paper, we address the simultaneous determination of price and inventory replenishment when customers return product to the firm. We examine cases when the quantity of returned product is a function of both the quantity sold and the price, in single and multi-period problems, with and without uncertainty in demand.     

Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.     

滑雪场季卡定价促销模型研究

根据06~07年间全国主要滑雪场的门市价和季卡价,首先运用EVIEWS6计量软件做出散点图、残差分析图以及残差的自相关-偏相关图,然后运用最小二乘估计方法确定回归方程系数,建立回归和序列组合模型,并将滑雪场的门市价代入相应方程计算出季卡付费方式下滑雪场应制定的最优价格,最后做相应的误差分析并总结本文模型的优点与不足.     

Option Pricing for Log-Symmetric Distributions of Returns

We derive an option pricing formula on assets with returns distributed according to a log-symmetric distribution. Our approach is consistent with the no-arbitrage option pricing theory: we propose the natural risk-neutral measure that keeps the distribution of returns in the same log-symmetric family reflecting thus the specificity of the stock’s returns. Our approach also provides insights into the Black–Scholes formula and shows that the symmetry is the key property: if distribution of returns X is log-symmetric then 1/X is also log-symmetric from the same family. The proposed options pricing formula can be seen as a generalization of the Black–Scholes formula valid for lognormal returns. We treat an important case of log returns being a mixture of symmetric distributions with the particular case of mixtures of normals and show that options on such assets are underpriced by the Black–Scholes formula. For the log-mixture of normal distributions comparisons with the classical formula are given.      

Heavy-tails and regime-switching in electricity prices

In this paper we first analyze the stylized facts of electricity prices, in particular, the extreme volatility and price spikes which lead to heavy-tailed distributions of price changes. Then we calibrate Markov regime-switching (MRS) models with heavy-tailed components and show that they adequately address the aforementioned characteristics. Contrary to the common belief that electricity price models ‘should be built on log-prices’, we find evidence that modeling the prices themselves is more beneficial and methodologically sound, at least in case of MRS models.     

An EOQ model for perishable products with discounted selling price and stock dependent demand

A single item economic order quantity model is considered in which the demand is stock dependent. After a certain time the product starts to deteriorate and due to visualization effect and other aspects of deterioration the demand becomes constant. In that situation a discount on selling price provides significant increment in demand rate. In this paper we investigate how much discount on selling price may be given during deterioration to maximize the profit per unit time and whether a pre-deterioration discount affects the unit profit or not. A mathematical model is developed incorporating both pre- and post deterioration discounts on unit selling price, where analytical results reveal some important characteristics of discount structure. A numerical example is presented and sensitivity analysis of the model is carried out.     

预期性后悔和欣喜作用下的最优序贯搜索策略研究

根据经济学中的后悔理论,首次在经典的最优序贯搜索问题中引入了决策者在搜索过程中的后悔和欣喜心理. 模型发现,如果决策者具备完美预期,那么她对后悔和欣喜的敏感度之差将直接决定她的搜索行为与最优搜索的偏差程度和方向,并且对于预期性后悔的敏感度越大则搜索程度越低. 这符合实验文献里“搜索过少”的结论. 进一步分析发现,在停止搜索后能知晓反事件价格的情况下,带有预期性后悔和欣喜的搜索将会趋向于经典的最优搜索策略. 如果对于后悔和欣喜的敏感度会受到搜索过程中经历过的类似心理的影响,模型对价格召回也作出了合理解释.