Option Pricing and Hedging under a Markov Switching Lévy Process Model

In this paper, we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging. In this model, the market interest rate, the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process. We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure. The option price using this model is obtained by the Fourier transform method. We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging.

Application of Exponential Distribution in Modeling of State Holding Time in HIV/AIDS Transition Dynamics

Markov modeling of HIV/AIDS progression was done under the assumption that the state holding time (waiting time) had a constant hazard. This paper discusses the properties of the hazard function of the Exponential distributions and its modifications namely;Parameter proportion hazard (PH) and Accelerated failure time models (AFT) and their effectiveness in modeling the state holding time in Markov modeling of HIV/AIDS progression with and without risk factors. Patients were categorized by gender and age with female gender being the baseline. Data simulated using R software was fitted to each model, and the model parameters were estimated. The estimated P and Z values were then used to test the null hypothesis that the state waiting time data followed an Exponential distribution. Model identification criteria;Akaike information criteria (AIC), Bayesian information criteria (BIC), log-likelihood (LL), and R2 were used to evaluate the performance of the models. For the Survival Regression model, P and Z values supported the non-rejection of the null hypothesis for mixed gender without interaction and supported the rejection of the same for mixed gender with interaction term and males aged 50 - 60 years. Both Parameters supported the non-rejection of the null hypothesis in the rest of the age groups. For Gender male with interaction both P and Z values supported rejection in all the age groups except the age group 20 - 30 years. For Cox Proportional hazard and AFT models, both P and Z values supported the non-rejection of the null hypothesis across all age groups. The P-values for the three models supported different decisions for and against the Null hypothesis with AFT and Cox values supporting similar decisions in most of the age groups. Among the models considered, the regression assumption provided a superior fit based on (AIC), (BIC), (LL), and R2 Model identification criteria. This was particularly evident in age and gender subgroups where the data exhibited non-proportional hazards and violated the assumptions required for the Cox Proportional Hazard model. Moreover, the simplicity of the regression model, along with its ability to capture essential state transitions without over fitting, made it a more appropriate choice.

数字化前后人民币汇率动态特征和路径转变分析——基于三机制Markov转换模型

通过邹氏断点检验建立人民币/美元汇率的三机制Markov转换自回归模型,选取2019年6月25日—2021年4月30日的人民币/美元汇率数据,将2020年5月29日作为人民币数字化的节点,实证分析数字人民币发展前后两个阶段的汇率机制转换特征;采用主观层次分析法计算数字人民币对当前金融体系各项指标的影响权重,分析数字人民币的发展对当前金融体系的影响程度。结果表明:数字人民币推进前,汇率在各机制上停留时间具有连续性,且均表现出高度“自维持性”;数字人民币推进后,汇率的动态转换较频繁,对外部信息冲击的反映较强烈。数字人民币进程的稳步推进对当前金融体系各方面带来不同程度的影响,对汇率的影响较明显。

Stochastic Model for Multiple Classes and Subclasses Simple Documents Processing

The issue of document management has been raised for a long time, especially with the appearance of office automation in the 1980s, which led to dematerialization and Electronic Document Management (EDM). In the same period, workflow management has experienced significant development, but has become more focused on the industry. However, it seems to us that document workflows have not had the same interest for the scientific community. But nowadays, the emergence and supremacy of the Internet in electronic exchanges are leading to a massive dematerialization of documents;which requires a conceptual reconsideration of the organizational framework for the processing of said documents in both public and private administrations. This problem seems open to us and deserves the interest of the scientific community. Indeed, EDM has mainly focused on the storage (referencing) and circulation of documents (traceability). It paid little attention to the overall behavior of the system in processing documents. The purpose of our researches is to model document processing systems. In the previous works, we proposed a general model and its specialization in the case of small documents (any document processed by a single person at a time during its processing life cycle), which represent 70% of documents processed by administrations, according to our study. In this contribution, we extend the model for processing small documents to the case where they are managed in a system comprising document classes organized in subclasses;which is the case for most administrations. We have thus observed that this model is a Markovian ML×K/ML×K/1 queues network. We have analyzed the constraints of this model and deduced certain characteristics and metrics. In fine, the ultimate objective of our work is to design a document workflow management system, integrating a component of global behavior prediction.

Comparisons of Maximum Likelihood Estimates and Bayesian Estimates for the Discretized Discovery Process Model

A Bayesian approach using Markov chain Monte Carlo algorithms has been developed to analyze Smith’s discretized version of the discovery process model. It avoids the problems involved in the maximum likelihood method by effectively making use of the information from the prior distribution and that from the discovery sequence according to posterior probabilities. All statistical inferences about the parameters of the model and total resources can be quantified by drawing samples directly from the joint posterior distribution. In addition, statistical errors of the samples can be easily assessed and the convergence properties can be monitored during the sampling. Because the information contained in a discovery sequence is not enough to estimate all parameters, especially the number of fields, geologically justified prior information is crucial to the estimation. The Bayesian approach allows the analyst to specify his subjective estimates of the required parameters and his degree of uncertainty about the estimates in a clearly identified fashion throughout the analysis. As an example, this approach is applied to the same data of the North Sea on which Smith demonstrated his maximum likelihood method. For this case, the Bayesian approach has really improved the overly pessimistic results and downward bias of the maximum likelihood procedure.

Towards an Intelligent Predictive Model for Analyzing Spatio-Temporal Satellite Image Based on Hidden Markov Chain

Nowadays remote sensing is an important technique for observing Earth surface applied to different areas such as, land use, urban planning, remote monitoring, real time deformation of the soil that can be associated with earthquakes or landslides, the variations in thickness of the glaciers, the measurement of volume changes in the case of volcanic eruptions, deforestation, etc. To follow the evolution of these phenomena and to predict their future states, many approaches have been proposed. However, these approaches do not respond completely to the specialists who process yet more commonly the data extracted from the images in their studies to predict the future. In this paper, we propose an innovative methodology based on hidden Markov models (HMM). Our approach exploits temporal series of satellite images in order to predict spatio-temporal phenomena. It uses HMM for representing and making prediction concerning any objects in a satellite image. The first step builds a set of feature vectors gathering the available information. The next step uses a Baum-Welch learning algorithm on these vectors for detecting state changes. Finally, the system interprets these changes to make predictions. The performance of our approach is evaluated by tests of space-time interpretation of events conducted over two study sites, using different time series of SPOT images and application to the change in vegetation with LANDSAT images.

DURATION OF NEGATIVE SURPLUS FOR A TWO STATE MARKOV-MODULATED RISK MODEL

We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.

Multiyear Discrete Stochastic Programming with a Fuzzy Semi-Markov Process

Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.

Modeling the Dynamics of the Random Demand Inventory Management System

At any given time, a product stock manager is expected to carry out activities to check his or her holdings in general and to monitor the condition of the stock in particular. He should monitor the level or quantity available of a given product, of any item. On the basis of the observation made in relation to the movements of previous periods, he may decide to order or not a certain quantity of products. This paper discusses the applicability of discrete-time Markov chains in making relevant decisions for the management of a stock of COTRA-Honey products. A Markov chain model based on the transition matrix and equilibrium probabilities was developed to help managers predict the likely state of the stock in order to anticipate procurement decisions in the short, medium or long term. The objective of any manager is to ensure efficient management by limiting overstocking, minimising the risk of stock-outs as much as possible and maximising profits. The determined Markov chain model allows the manager to predict whether or not to order for the period following the current period, and if so, how much.

多重防护机制下LNG动力船风险态势分析方法

为探讨多重防护机制下的液化天然气(Liquefied Natural Gas,LNG)动力船营运风险特征,提出了一种基于复杂性控制系统作用模式的风险态势分析方法。从系统控制过程视角,采用系统控制过程分析方法(System-Theoretic Process Analysis,STPA)确立LNG动力船系统安全控制的风险致因,揭示基于LNG泄漏三重防护机制的风险因子体系和风险形成机制;引入隐马尔可夫模型(Hidden Markov Model,HMM),进行无监督学习并确立模型参数,推理多重防护机制下的LNG动力船风险转移特征;结合LNG动力船营运的具体场景,对三重防护机制分别进行仿真并统计风险态势。仿真结果表明,三重防护机制在降低LNG动力船营运风险态势方面具有因子诱导的针对性,在防漏因子、止漏因子和治漏因子诱导下LNG动力船分别趋向一般风险状态、较高风险状态和高风险状态。基于复杂性控制系统作用模式的风险态势分析可为LNG动力船营运的安全控制和风险管理提供管控模式和手段。

Conditional Value-at-Risk for Random Immediate Reward Variables in Markov Decision Processes

We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced using conditional value-at-risk for random immediate reward variables in Markov decision processes, under whose risk measure criteria the risk-optimal policies are characterized by the optimality equations for the discounted or average case. As an application, the inventory models are considered.

A Stochastic SIVS Epidemic Model Based on Birth and Death Process

A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.

基于HMM-MLP的泵站监测健康诊断系统研究

为实现泵站工程在生产运行过程中有效预测设备潜在故障风险,提升泵站设备运行效率,在数字孪生水利工程数据底板基础上,基于现有硬件设备,以结构故障机理为导向,提出了一种HMM-MLP的泵站设备故障预测方法。先由连续小波包变换处理设备的运行信号,然后通过HMM模型生成设备运行状态序列作为MLP网络的输入预测设备故障,最后通过仿真实验表明,HMM-MLP模型可有效提高泵站设备故障的预测准确率。同时,依托在线监测数据和离线检查与试验数据,建立了设备健康评价指标体系,并开发了泵站监测健康诊断系统,协助运行管理人员充分了解和掌握机组设备的“健康”状态,提升设备管理的信息化水平。结果表明:该研究可为泵站健康系统建设提供实际案例指导与经验启示。

主接线可靠性评估中断路器的 Markov 可靠性等效模型

本文在应用Ｍａｒｋｏｖ过程对变电主接线进行可靠性评估的过程中，对其中的主要元件断路器进行了专门讨论，深入阐述了断路器在运行中可能出现的各种故障，并运用Ｍａｒｋｏｖ过程的基本理论，对其经故障统计得出的原始状态空间图按正常、拒动、其它扩大型故障（除拒动外）和非扩大型故障进行状态合并、得到能全面反映断路器各种故障模式的可靠性等效模型。

基于Markov模型的铝土矿露天采空区生态重建的环境预测评价

采用景观生态空间结构预测分析法对平果铝土矿生态重建的环境影响进行评价;在建立空间格局变化定量指标的基础上,利用Markov过程稳定状态方程组的随机运动过程数学模型,对平果铝土矿生态重建地区环境影响进行预测评价。研究结果表明:2005年预测模拟值与实测情况基本吻合,当矿区复垦土地的裸岩地面积减少到占总土地面积的19.92%时,矿区生态系统达到稳定状态,Markov过程模型对喀斯特石漠化地区环境影响预测与评价是可行的。

加权合成的嵌入式隐Markov模型人脸识别

嵌入式隐 Markov模型能提取人脸的二维主要特征并对姿态和环境的变化具有较好鲁棒性 .讨论了嵌入式隐 Markov模型的进一步改进及其实现 .首先分析了形成观察向量的采样窗大小和其二维 DCT系数项数的不同对人脸识别结果的影响 ,然后确定最优的采样窗大小和其二维 DCT系数项数 .鉴于不同角度的照片包含信息量的不同 ,提出了一种加权合成的模型参数重估算法 .重估模型参数时 ,首先计算每幅脸像相对应的模型参数 ,然后进行加权合并 ,权值由迭代公式求得 ,训练结束后用一个合成的模型来表示一个对象 .采用基于该方法的原型系统对 ORL人脸库进行测试 ,识别正确率达到了 99.5 % .

随机模型检测连续时间Markov过程

功能正确和性能可满足是复杂系统可信要求非常重要的两个方面。从定性验证和定量分析相结合的角度,对复杂并发系统进行功能验证和性能分析,统一地评估系统是否可信。连续时间Markov决策过程CTMDP(Continu-ous-time Markov decision process)能够统一刻画复杂系统的概率选择、随机时间及不确定性等重要特征。提出用CT-MDP作为系统定性验证和定量分析模型,将复杂系统的功能验证和性能分析转化为CTMDP中的可达概率求解,并证明验证过程的正确性,最终借助模型检测器MRMC(Markov Reward Model Checker)实现模型检测。理论分析表明,提出的针对CTMDP模型的验证需求是必要的,验证思路和方法具有可行性。

基于Markov决策过程的驾驶员行为模型

将驾驶员-汽车看作统一的人机系统,利用驾驶员驾驶过程的本质是决策过程的性质,通过确定系统的决策时刻、决策报酬、状态转移速率和概率、抽象驾驶员的行为集合等建立了基于Markov决策过程的驾驶员行为模型,最后对所建模型进行了计算机仿真。

移动机器人Markov定位算法的研究——方向传感器建模新方法

为了改善移动机器人Markov定位算法中方向传感器模型的性能,提出基于高斯函数的新概率模型.该模型考虑了方向角周期性问题,对相位进行了转换,利用高斯函数对方向传感器进行了概率建模.将此模型放入Markov算法,与其他传感器组成观测模型,并进行对称环境中的单次定位仿真和复杂环境中的连续定位仿真.仿真结果表明,这种概率模型计算量小,收敛速度快,在大量测量噪声存在下工作稳定.

面向城市建成区扩展模拟的CA-Markov模型改进

对城市建成区扩展的预测是防止城市蔓延的重要管理依据。目前,元胞自动机-马尔可夫链模型,已成为城市建成区扩展预测的重要方法。该模型对指标权重的赋值方法较为敏感,以往的单一指标赋值法,影响了城市建成区扩展预测的精度和可信度。为此,本研究提出整合传统权重赋值法的AHP和逻辑回归模型改进CA-Markov模型。研究选择云南省大理市为案例,对2020、2030年的城市建成区扩展进行模拟和预测,最后进行精度验证。研究结果表明:(1)Kappa指数可达到96.8%,预测结果有较好的一致性。(2)大理市的城市建成区扩展均表现为继续向外扩展,以东南、西北方向和两片建成区之间为主要扩展方向。研究提供了组合权重赋值法改进CA-Markov模型,这将为规划者在未来规划中提供强有力的支持。