Pricing Catastrophe Options with Credit Risk in a Regime-Switching Model

In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space.By using the measure change technique,we derive the price expressions of catastrophe put options.Moreover,we conduct some numerical analysis to demonstrate how the parameters of the model affect the price of the catastrophe put option.

On Optimal Proportional Reinsurance and Investment in a Markovian Regime-Switching Economy

In this paper, the surplus of an insurance company is modeled by a Markovian regime- switching diffusion process. The insurer decides the proportional reinsurance and investment so as to increase revenue. The regime-switching economy consists of a fixed interest security and several risky shares. The optimal proportional reinsurance and investment strategies with no short-selling constraints for maximizing an exponential utility on terminal wealth are obtained.

Dynamics of Non-Markovianity, Quantum Correlations and Information Scrambling of Three Qubits Systems Interacting via Rashba Interaction

The behavior of the quantum correlations, information scrambling and the non-Markovianity of three entangling qubits systems via Rashba is discussed. The results showed that, the three physical quantities oscillate between their upper and lower bounds, where the number of oscillations increases as the Rashba interaction strength increases. The exchanging rate of these three quantities depends on the Rashba strength, and whether the entangled state is generated via direct/indirect interaction. Moreover, the coherence parameter can be used as a control parameter to maximize or minimize the three physical quantities.

Optimal mean-variance reinsurance and investment strategy with constraints in a non-Markovian regime-switching model

This paper is devoted to study the proportional reinsurance/new business and investment problem under the mean-variance criterion in a continuous-time setting.The strategies are constrained in the non-negative cone and all coefficients in the model except the interest rate are stochastic processes adapted the filtration generated by a Markov chain.With the help of a backward stochastic differential equation driven by the Markov chain,we obtain the optimal strategy and optimal cost explicitly under this non-Markovian regime-switching model.The cases with one risky asset and Markov regime-switching model are considered as special cases.

Practical stability and instability of regime-switching diffusions

This work is devoted to practical stability of a class of regime-switching diffusions. First, the notion of practical stability is introduced. Then, sufficient conditions for practical stability and practical instability in probability and in pth mean are provided using a Lyapunov function argument. In addition, easily verifiable conditions on drift and diffusion coefficients are also given. Moreover, examples are supplied for demonstration purposes.

Bayesian Markov Regime-Switching Models for Cointegration

This paper introduces a Bayesian Markov regime-switching model that allows the cointegration relationship between two time series to be switched on and off over time. Unlike classical approaches for testing and modeling cointegration, the Bayesian Markov switching method allows for estimation of the regime-specific model parameters via Markov Chain Monte Carlo and generates more reliable estimation. Inference of regime switching also provides important information for further analysis and decision making.

Lyapunov-Based Output Containment Control of Heterogeneous Multi-Agent Systems With Markovian Switching Topologies and Distributed Delays

This paper considers the mean square output containment control problem for heterogeneous multi-agent systems(MASs)with randomly switching topologies and nonuniform distributed delays.By modeling the switching topologies as a continuous-time Markov process and taking the distributed delays into consideration,a novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders'states.A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays.By constructing a novel switching Lyapunov functional,the output containment control problem is then solved in the sense of mean square under an easily-verifiable sufficient condition.Finally,two numerical examples are given to show the effectiveness of the proposed controller.

Goal Achieving Probabilities of Mean-Variance Strategies in a Market with Regime-Switching Volatility

In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.

基于PI的Semi-Markovian电力系统事件触发控制设计分析

基于PI控制器设计理论,本文对电力系统负荷频率的稳定性问题进行分析,提出改进的事件触发机制,对带有不确定性半马尔可夫跳变参数的电力系统进行数学均值期望处理,整理构建成随采样信号状态变化而自适应调整的闭环系统。考虑随机跳变多模态下系统中的干扰影响和时滞虚拟延迟,设计模态依赖控制器,结合矩阵叉积不等式和Schur补定理等,对泛函导数积分项进行放缩,将最优值问题转化为解线性矩阵不等式,最终利用Matlab工具箱求解,求出控制增益和事件触发矩阵,给出系统随机稳定性判据,对系统H∞性能指标进行分析。本文所设计方案可以提高通信网络中控制信号的传输率,有效减轻电网信息输送负担,在节约能源的同时还能提高系统的动态性能。

HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING

In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter H is supposed to be in(1/2, 1). As a direct application, the strong Feller property is presented.

Reachable set estimation for discrete-time Markovian jump neural networks with unified uncertain transition probability

This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay.By allowing uncertainty in the transition probabilities,a framework unifies and enhances the generality and realism of these systems.To fully exploit the unified uncertain transition probabilities,an equivalent transformation technique is introduced as an alternative to traditional estimation methods,effectively utilizing the information of transition probabilities.Furthermore,a vector Wirtinger-based summation inequality is proposed,which captures more system information compared to existing ones.Building upon these components,a novel condition that guarantees a reachable set estimation is presented for Markovian jump neural networks with unified uncertain transition probabilities.A numerical example is illustrated to demonstrate the superiority of the approaches.

具有Markovian时延与丢包的离散系统的状态估计

网络化控制系统中经常会因网络带宽有限而导致数据包在网络中传输时产生时延甚至丢失.本文主要研究具有Markovian时延与丢包的离散线性系统的状态估计问题.通过在估计器端设置适当长度的缓存器,把具有多状态Markovian时延与丢包的离散定常系统建模成数据包到达过程为两状态Markovian模型的离散时变系统,并基于跳跃线性估计器的思想提出了一类特殊的估计器,即限定接收历史估计器(FRHE).在最大时延已知时,给出了可选增益的最优FRHE设计策略.该策略虽然是次优,却能提供简便的计算.通过与时变Kalman估计器(TVKE)的仿真对比,表明所提策略的有效性.

带Poisson跳和Markovian转换的随机时滞泛函微分方程数值解的收敛性（英文）

为了近一步研究带Poisson跳和Markovian转换的随机时滞泛函微分方程数值解的收敛性问题,文中给出带Poisson跳和Markovian转换的随机时滞泛函微分方程Euler数值解迭代格式.在弱条件下,利用Laypunov泛函方法和随机分析理论证明了数值解依概率收敛于方程的解.所得结果覆盖了许多非线性时滞微分方程已经存在的某些理论,而且实验说明此结论比以往的结论更容易验证.

Markovian模型在供应链合同管理中的应用

为达到供应链绩效更优,供应链节点企业,在合作基础上,即要保证双方利益,又要保证供应链绩效,进行谈判、签定各种供应合同,当采购商需求、供应商生产不确定的情况下,谈判人员必须依靠有效、快速的评价方法获得有效供应链合同,本文总结了供应链中主要的几种供应链合同模型,并以定量供应链合同为例,运用Markovian模型评判最优决策方案,为谈判人员谈判决策提供参考依据。

一类不确定非线性2-D Markovian跳跃系统的鲁棒随机镇定

考虑在Roesser模型中带有一类广义的Lipschitz非线性部分的不确定2-D Markovian跳跃参数系统的鲁棒镇定问题。在假设不确定的参数范数有界的前提下,设计状态反馈控制器,使得闭环系统对于所有允许的不确定性总是渐近稳定的。运用线性矩阵不等式(LMIs),给出了解决问题的充分条件。通过求解一定的LMIs,得到所需的状态反馈控制器。一个数值算例说明了所提出理论的有效性。

离散Markovian跳变系统概率转移矩阵部分未知的可靠控制

针对执行器故障和概率转移矩阵部分未知的情况,研究了一类离散Markovian跳变系统的可靠控制问题.设计有效的状态反馈可靠控制器,不仅使得闭环系统在无故障的情况下是随机稳定的,而且在执行器出现故障的情况下还仍然使得闭环系统是随机稳定的.用一组耦合可解的线性矩阵不等式给出了可靠控制器的可行性条件.数值算例表明了所提方法的可行性和有效性.

带有时滞和脉冲的Markovian跳变神经网络的同步

研究一类带有时滞和脉冲的Markovian跳变神经网络的同步问题,其中跳变参数为连续时间离散状态的Markovian过程。基于Lyapunov-Krasovskii泛函以及线性矩阵不等式方法,得到了带有时滞和脉冲的Markovian跳变神经网络的均方同步条件,并通过数值仿真验证了所得结论。

带分数布朗运动和Markovian跳的种群系统的近优控制

讨论了一类带有分数布朗运动和Markovian调制的随机种群系统最优逼近控制问题,给出了模型的伴随方程、哈密顿函数,应用Ekeland变分原理、Ito公式及一些不等式给出了随机种群系统最优逼近控制存在的必要条件.

噪声诱导的量子相干性保护

为了有效克服量子退相干,本文提出通过引入额外噪声来保护量子相干性的方法,将Jaynes-Cummings(J-C)模型耦合到外部非马尔可夫玻色子库模型,利用缀饰态方法求解此模型,并在随机耦合的情况下对许多随机轨迹进行数值平均,计算系统的密度矩阵。数值计算表明,原子与腔耦合中的随机噪声可以有效抑制腔泄漏引起的弛豫和退相干效应,噪声的记忆时间对量子相干性保护产生重要影响。此研究为利用噪声保护量子相干性提供一条新路径。

离散Markovian跳变系统模态依赖非脆弱H_∞控制

本文考虑待设计控制器增益存在乘性范数有界不确定摄动,研究了离散Markovian跳变系统在跳变参数可获得时的模态依赖非脆弱H∞控制问题.运用LMI技术推导出模态依赖非脆弱反馈H∞控制器存在的充要条件,并得到计算控制器参数的公式.最后针对一个具体数值算例进行了仿真,通过测取状态响应和输出响应曲线,并与不考虑控制器参数摄动的常规H∞反馈控制器设计结果相比较,展示了本文方法的有效性.