周期过程的模型识别

具有某种周期性规律的随机过程,在概率统计意义上,属于非平稳过程。通过多阶差分方法可将这类过程的随机序列变换为与其相对应的平稳随机序列。用统计相关函数法可以确定平稳随机序列的合适的数学模型。文中以电力系统负荷变化过程为例,介绍了具体算法并列出了部分结果。     

一类与半鞅有关的推广型脉冲控制(I)

本篇首次将关于半鞅的随机微分方程的解过程引入平稳型脉冲控制的状态结构,建立了一种新的模型,从而实质性地推广了此前的各类平稳型脉冲随机控制模型.本篇通过新的分析手法证明了与新模型相关的变分方程解的存在性,这种新方法比以前类似问题的分析方法更直接、更明快.     

一类与半鞅有关的推广型脉冲控制(Ⅰ)

本篇首次将关于半鞅的随机微分方程的解过程引入平稳型脉冲控制的状态结构, 建立了一种新的模型,从而实质性地推广了此前的各类平稳型脉冲随机控制模型.本篇 通过新的分析手法证明了与新模型相关的变分方程解的存在性,这种新方法比以前类似 问题的分析方法更直接、更明快.     

一类半鞅状态的平稳型脉冲随机控制

本文提出了一类新的随机控制模型,这类模型不但在费用结构上推广了此前的平稳型脉冲随机控制,而且首次将一类半鞅引入脉冲控制模型的状态结构从而推广了相应的状态过程.通过对一类相当复杂的变分方程问题的研究并利用其有关结论,我们证明了新模型最佳控制的存在性并刻划出其结构.     

带停时的奇异型随机控制问题研究

利用随机分析的知识及最优控制理论,推广了一类带停时的随机控制问题,针对不同参数,证明了最佳控制的存在性,分两种情况给出了最佳控制的存在区域,并给出了不同初始状态下,最佳控制的结构和最佳费用函数.由于将原模型中费用结构中的R-S积分的被积函数由1推广为满足某些条件的一般函数,所以推广后的模型更具一般性.     

非平稳过程的小波因果度量

该文对带有随机趋势的非平稳过程给出了一种新的因果度量定义.作者将证明新定义与Hosoya给出的因果度量定义等价, 但由于避免了以往文献中常见的对非平稳过程协整性的要求, 该定义有利于简化因果关系的假设检验.文中还对Wald检验和似然比检验进行了讨论.数值模拟和实证分析表明, 这两种检验方法都是有效的.     

一类脉冲控制最佳费用的解析表达式

§1.导言 脉冲控制是一种重要类型的随机控制,其实用价值及理论意义都很大,故已有很多文章对其各种模型从不同角度进行各种研究,比如[1]—[3]等.但在过去的这些研究中,或是只给了最佳控制存在的充分条件,或是证明了最佳控制的存在性,但最佳费用函数却     

一类脉冲型平稳最佳随机控制之研究

本文研究了一类平稳的脉冲控制模型，不仅证明了最佳脉冲控制的存在性而且构造出一个最佳控制．     

最佳控制的数学問题(Ⅲ)

本文前两部分已用动态規划和最大原則方法討論了最佳控制的数学問題;这两种方法以及变分学方法是現時解决这类問題的基本工具。然而,近年来有些作者又提出另一些办法;文献是其中之一。n阶线性系統的离散最佳控制問題可以变換为一个非线性規划问題,因此,非线性規划方法为这类問題的数值解提供一个算法;同时他引出利用解-空間来分析最佳控制問題的观点。以下的討論引用了这位作者的一部分工作。     

可分离随机过程的新息与滤波

本文定义了连续时间二阶随机过程的某种可分离性,给出了这类过程的新息过程所满足的关系式,并且证明了它们与“白噪声”作用下的线性系统的输出过程等价.又给出了一类与上述过程具有某种可分离性的随机向量的最佳线性估计.作为应用,严格地推导了两种线性系统的新息、滤波、预报和平滑所满足的随机微分方程.     

Optimal proportional reinsurance and investment for stochastic factor models

In this work we investigate the optimal proportional reinsurance-investment strategy of an insurance company which wishes to maximize the expected exponential utility of its terminal wealth in a finite time horizon. Our goal is to extend the classical Cramér–Lundberg model introducing a stochastic factor which affects the intensity of the claims arrival process, described by a Cox process, as well as the insurance and reinsurance premia. The financial market is supposed not influenced by the stochastic factor, hence it is independent on the insurance market. Using the classical stochastic control approach based on the Hamilton–Jacobi–Bellman equation we characterize the optimal strategy and provide a verification result for the value function via classical solutions to two backward partial differential equations. Existence and uniqueness of these solutions are discussed. Results under various premium calculation principles are illustrated and a new premium calculation rule is proposed in order to get more realistic strategies and to better fit our stochastic factor model. Finally, numerical simulations are performed to obtain sensitivity analyses.     

Optimal control of random evolutions

We consider a stochastic control problem for a random evolution. We study the Bellman equation of the problem and we prove the existence of an optimal stochastic control which is Markovian. This problem enables us to approximate the general problem of the optimal control of solutions of stochastic differential equations.     

Discrete and sampled-data stochastic control problems with complete and incomplete state information

An unconstrained stochastic optimization problem involving a discrete-time linear process with a normally distributed initial condition and subject to additive gaussian state and measurement noise is formulated in terms of a quite general finite horizon, discrete-time quadratic cost criterion and solved when there is either complete or incomplete state information. It is shown that both the stochastic sampled-data optimal tracker and the stochastic sampled-data optimal regulator are special cases of this problem. A breakdown of the minimum cost for both sampled-data controllers is given.     

有限时区上的最优转换和停止问题

讨论了有限时区上的最优转换和停止问题,它是一类同时具备脉冲控制和最优停止特征的最优控制问题.问题的最优值以及最优转换和停止决策可以由具有混合障碍的多维反射倒向随机微分方程的解来刻画.接着考虑了形式更一般的反射倒向随机微分方程并证明了方程解的存在唯一性.     

有限时区上的最优转换和停止问题

讨论了有限时区上的最优转换和停止问题,它是一类同时具备脉冲控制和最优停止特征的最优控制问题.问题的最优值以及最优转换和停止决策可以由具有混合障碍的多维反射倒向随机微分方程的解来刻画.接着考虑了形式更一般的反射倒向随机微分方程并证明了方程解的存在唯一性.     

Optimal non-proportional reinsurance control

This paper deals with the problem of ruin probability minimization under various investment control and reinsurance schemes. We first look at the minimization of ruin probabilities in the models in which the surplus process is a continuous diffusion process in which we employ stochastic control to find the optimal policies for reinsurance and investment. We then focus on the case in which the surplus process is modeled via a classical Lundberg process, i.e. the claims process is compound Poisson. There, the optimal reinsurance policy is derived from the Hamilton-Jacobi-Bellman equation.     

Optimal resource allocation across related channels

In this paper, we consider resource allocation strategies of a limited resource across two related channels in a multi-period setting. We study a stochastic control problem where the objective is to determine the optimal limited resource allocation policy across two related channels and optimal transshipment policy between these two channels. We characterize some structural results of the optimal resource allocation policy and show that it is determined by three monotone curves.     

HARA frontiers of optimal portfolios in stochastic markets

In this paper, we consider the optimal portfolio selection problem in continuous-time settings where the investor maximizes the expected utility of the terminal wealth in a stochastic market. The utility function has the structure of the HARA family and the market states change according to a Markov process. The states of the market describe the prevailing economic, financial, social and other conditions that affect the deterministic and probabilistic parameters of the model. This includes the distributions of the random asset returns as well as the utility function. We analyzed Black–Scholes type continuous-time models where the market parameters are driven by Markov processes. The Markov process that affects the state of the market is independent of the underlying Brownian motion that drives the stock prices. The problem of maximizing the expected utility of the terminal wealth is investigated and solved by stochastic optimal control methods for exponential, logarithmic and power utility functions. We found explicit solutions for optimal policy and the associated value functions. We also constructed the optimal wealth process explicitly and discussed some of its properties. In particular, it is shown that the optimal policy provides linear frontiers.     

On a problem of optimal harvesting from a stochastic system with a jump component

In this paper, we study a problem of optimal harvesting from a stochastic system modeled by a geometric Lévy process. A verification theorem of the variational inequality type is also given and proved. The paper has been motivated by I. Elsanosi et al. [Stochastics Stochastics Rep. (2000)], where the authors considered an optimal harvesting problem with price dynamics following a stochastic differential delay equation.