固定支出下最优资产组合策略

在固定消费支出水平的条件之下,文章就资产组合问题建立常方差弹性（CEV）模型,应用随机控制原理求出了相应的非线性Hamilton—Jacobi—Bellman偏微方程,再用Legendre变换将其转化为线性偏微方程,建立对偶问题。通过对偶问题的求解,从而求得原问题的精确解析解,确定风险资产和无风险资产的最优投资比例,实现了满足既定支出水平下总资产的对数效用最大化,从实际市场的角度改进发展了经典的Merton模型结果．     

基于CEV过程带交易费的脆弱期权定价的数值算法

主要研究基于CEV过程且支付交易费的脆弱期权定价的数值计算问题.首先通过构造无风险投资组合,导出了基于CEV过程且支付交易费用的脆弱期权定价的偏微分方程模型;其次应用有限差分方法将定价模型离散化,并设计数值算法;最后以看跌期权为例进行数值试验,分析各定价参数对看跌期权价值的影响.     

Coexistence states of a three-species cooperating model with diffusion

In this article, a Lotka--Volterra three-species time-periodic mutualism model with diffusion is investigated. Some sufficient conditions for the existence and estimates of coexistence states are established. Meanwhile, with the assistance of functional analysis methods, some sufficient or necessary results for the existence of positive steady state of the model are presented. Our approach to the discussion is mainly based on the skill of sub- and super-solutions for a general reaction--diffusion system.     

CEV模型下美式期权的差分算法

假设标的股价服从不变方差弹性(CEV)模型下,推导出美式看跌期权所遵循的变分不等方程.利用显式有限差分格式,给出具体的数值算法,并对格式的适定性进行分析,最后将其应用于实例,验证了算法的有效性.     

固定支付下养老基金资产组合CEV模型及最优投资策略

在固定支付水平的条件之下,就养老基金资产组合问题建立常方差弹性(CEV)模型,应用随机控制原理求出了相应的非线性Hamilton-Jacobi-Bellman偏微方程,再用Legendre变换将其转化为线性偏微方程,建立对偶问题.通过对偶问题的求解,从而求得原问题的精确解析解,确定风险资产和无风险资产的最优投资比例,实现了满足养老基金既定支出水平下总资产的对数效用最大化,从实际市场的角度改进发展了经典的Merton模型结果.     

CEV模型下家庭最优投资决策问题

考虑固定收入下具有随机支出风险的家庭最优投资组合决策问题.在假设投资者拥有工资收入的同时将财富投资到一种风险资产和一种无风险资产,其中风险资产的价格服从CEV模型,无风险利率采用Vasicek随机利率模型.当支出过程是随机的且服从跳-扩散风险模型时,运用动态规划的思想建立了使家庭终端财富效用最大化的HJB方程,采用Le...     

Time-consistent mean–variance proportional reinsurance and investment problem in a defaultable market

In this paper, we consider an optimal time-consistent reinsurance-investment problem incorporating a defaultable security for a mean–variance insurer under a constant elasticity of variance (CEV) model. In our model, the insurer’s surplus process is described by a jump-diffusion risk model, the insurer can purchase proportional reinsurance and invest in a financial market consisting of a risk-free asset, a defaultable bond and a risky asset whose price process is assumed to follow a CEV model. Using a game theoretic approach, we establish the extended Hamilton–Jacobi–Bellman system for the post-default case and the pre-default case, respectively. Furthermore, we obtain the closed-from expressions for the time-consistent reinsurance-investment strategy and the corresponding value function in both cases. Finally, we provide numerical examples to illustrate the impacts of model parameters on the optimal time-consistent strategy.     

CEV模型和B-P混合驱动模型下亚式期权Monte Carlo模拟

对亚式期权在CEV模型和B-P混合驱动模型限制下进行Monte Carlo模拟定价,建立风险中性测度,模拟出不同弹性因子值下资产价格路径.为了得出优于标准的Monte Carlo模拟,应用方差缩减技术来提高期权定价的精度.最后对亚式期权定价模型进行数值案例分析,得出弹性因子取值、时间步长、模拟次数与期权价值变化的关系.     

Portfolio selection problem with multiple risky assets under the constant elasticity of variance model

This paper focuses on the constant elasticity of variance (CEV) model for studying the utility maximization portfolio selection problem with multiple risky assets and a risk-free asset. The Hamilton-Jacobi-Bellman (HJB) equation associated with the portfolio optimization problem is established. By applying a power transform and a variable change technique, we derive the explicit solution for the constant absolute risk aversion (CARA) utility function when the elasticity coefficient is −1 or 0. In order to obtain a general optimal strategy for all values of the elasticity coefficient, we propose a model with two risky assets and one risk-free asset and solve it under a given assumption. Furthermore, we analyze the properties of the optimal strategies and discuss the effects of market parameters on the optimal strategies. Finally, a numerical simulation is presented to illustrate the similarities and differences between the results of the two models proposed in this paper.     

Optimal investment strategy for annuity contracts under the constant elasticity of variance (CEV) model

This paper focuses on the constant elasticity of variance (CEV) model for studying the optimal investment strategy before and after retirement in a defined contribution pension plan where benefits are paid under the form of annuities; annuities are supposed to be guaranteed during a certain fixed period of time. Using Legendre transform, dual theory and variable change technique, we derive the explicit solutions for the power and exponential utility functions in two different periods (before and after retirement). Each solution contains a modified factor which reflects an investor’s decision to hedge the volatility risk. In order to investigate the influence of the modified factor on the optimal strategy, we analyze the property of the modified factor. The results show that the dynamic behavior of the modified factor for the power utility mainly depends on the time and the investor’s risk aversion coefficient, whereas it only depends on the time in the exponential case.     

CEV和B&P作用下带交易费的亚式期权定价模型

基于B-S定价模型的基础,利用Ito公式及保值策略,研究了股票价格服从CEV模型和B&P过程且存在交易费用的亚式期权的定价模型.得出了该类期权价格所满足的微分方程,并对模型做了数值分析.结论拓宽了亚式期权的研究范围,更适用于实际金融市场.     

养老基金投资组合的常方差弹性(CEV)模型和解析决策

针对以年金形式发放待遇的缴费预定制养老基金,在退休前和退休后的两个阶段,分别构建了常方差弹性(CEV)模型,并应用Legendre变换将原问题转化为对偶问题,在追求指数效用最大化的条件下,求得了精确解析解,从而确定了这两个阶段的最优投资决策．     

Study on an ideal start-up model for a modified Scheibel column

The start-up process existed in every solvent extraction process. An optimal start-up strategy in the solvent extraction process can shorten the time to get to steady state greatly. In order to offer some useful methods for the study on the start-up in the extraction process, an ideal start-up model was developed for a modified Scheibel extraction column. The numerical solution for the multi-stage extraction system was obtained from solving the mathematical equations. From the calculated values, the relationships between variables and time were established. According to the relationships obtained above, suitable start-up strategy could be taken to drive the extraction system to the desired steady state.     

Positive Steady States of a Competitor- Competitor-Mutualist Model

In this paper we deal with the positive steady states of a Competitor-Competitor-Mutualist modelwith diffusion and homogeneous Dirichlet boundary conditions.We first give the necessary conditions,and thenestablish the sufficient conditions for the existence of positive steady states.     

一类广义扩散模型解的存在性

通过考虑具二阶导数项的Ｌａｎｄａｕ－Ｇｉｎｚｂｕｒｇ自由能量泛函,本文导出了一类广义扩散模型,进而采用经典的能量估计方法和对所引入的能量泛函进行精细的分析,获得了所论模型解的存在性和唯一性。     

Dynamic model of methane–water diffusion

This paper presents a mathematical model to describe the time evolution of the diffusion process of methane exchange between liquid and gaseous phases. In order to reach the equilibrium, the distribution of gas in the liquid phase decreases to a constant value over time. Generalized model is analyzed under the assumption that both, reversible and irreversible form of absorption and desorption, occur at the same time. For the application in case of the real system of methane–water, model is developed under the assumption that the processes of absorption and desorption are irreversible. From the experimental data are determined the coefficients of model and their dependence on initial conditions, with constant end conditions. This paper tests the introduced theoretical model on the existing experimental data.     

带干扰的双Poisson风险模型的破产概率

首先将[3]的双Possion风险模型推广到带干扰的一种新模型。然后运用鞅论的方法得出破产概率满足Lundberg不等式和一般公式。以及当个体所赔服从指数分布时的破产概率的具体表达式。