hjb

HJB Equations Subject to Stochastic Control Theory and Securities Investment Models

随机控制的HJB方程与证券投资模型

Through the dynamic programming principle , we got the HJB equation which the optimal policy should satisfy .

通过动态规划原理，我们得到了最优策略应该满足的HIB方程。

Abstract : This paper gives a proof of a comparison theorem on the viscosity solution of HJB Equation .

文摘：证明了与随机控制问题有关的动态规划方程粘性解的比较定理。

From the HJB equation satisfied by the value function V ( x ), we find the optimal stopping time τ .

通过建立值函数V（x）满足的HJB方程，我们找到了最优停止时刻τ。

Optimal strategies are obtained with an abstract form in general cases via HJB equation which is derived from dynamic programming principle and stochastic analysis .

给出了财富预算方程，运用动态规划原理及随机分析导出该问题的HJB方程，并由此得到一般情形下抽象形式的解。

Finally , based on the HJB equation and combining with the optimal stopping methodologies , the free boundary of the product price is obtained .

最后根据HJB方程，结合最优停时方法，得到产品价格的自由边界。

Conclusion Age , poor mastoid gasification and right side have obvious influence on the occurrence of HJB , while gender does not .

结论成人、乳突气化欠佳、右侧发生对颈静脉球窝高位发生有显著性影响，而性别则无显著性影响。

The HJB equation is then reduced to a set of recursive algebraic equations and yields a closed-loop controller with a finite number of terms .

HJB方程简化为一组递归的代数方程，求得一个有限项的闭环控制器。

In chapter 5 , we explicitly solve the HJB equation that is derived in chapter 4 and get an optimal strategy about the producing and stopping time .

第五章，精确地解出了第四章中得出的HJB方程，并给出生产和停时的最优策略。

By applying verification theorem to the HJB ( Hamilton_Jacobi_Bellman ) equation , the optimal strategies in an explicit form for initial control problem are presented .

应用验证性定理求解HJB（HamiltonJacobiBellman）方程得到了原问题的最优策略。

From the analysis of the HJB equation , the explicit results about the dividends is evident when the claim amount X , Y are all exponential distribution .

通过对HJB方程的分析，得出了当索赔额X，Y都服从指数分布时的详细结果。

Using the dynamic programming approach , an explicit solution to the value function of the optimal portfolio problem is obtained by the HJB equation , and the optimal investment strategy is given .

利用动态规划方法通过HJB方程得到最优投资组合价值函数的显式解，并给出最优投资策略。

This iterative algorithm starts from an initial performance index and converges to its optimal solution by updating the control and performance . It avoids solving the complex HJB equation directly .

该算法从初始性能指标函数开始迭代，经过控制律和性能指标的逐步更新，最终收敛到系统的最优性能指标，有效地避免了直接求解复杂的HJB方程。

The main idea is to discretize the model on time and state space , then the numerical solution of discrete HJB equation is used as approximation of the continuous HJB equation .

由于此方程的解析解较难得到，我们将采用近似方法，将模型在时间和状态空间上分别离散化，将离散最优控制问题的解作为连续模型的近似。

Applying dynamic program to the optimal control problem of this jump process , we obtain integro differential HJB equation . Since the analytical solution is difficult to get , we will find its numerical solution .

对这一跳跃过程最优控制问题，我们应用动态规划原理得到了积分-微分（integro-differential）形式的HJB方程。

Based on the definition of the value function and the coefficient of risk aversion , the nonlinear transformation of value function was proved to be in agreement with HJB partial differential equation with the coefficient of risk aversion .

根据值函数和风险规避系数的定义，说明经非线性变换后的值函数满足带有风险规避系数的HJB偏微分方程。

The HJB equation associated to the optimal investment problem becomes the semilinear partial differential equation by the logarithmic transformation . The existence of optimal portfolios solution is proved and the value function and optimal strategies are given .

通过对数变换将最优问题的HJB方程转化为半线性偏微分方程，证明了最优投资组合解的存在性，给出了价值函数和最优投资策略。

With the help of the dynamic programming principle and Lie algebra theory , we get the corresponding HJB equation , obtain the analytical expressions of the value function based on Lie symmetry , and present the optimal investment strategy .

借助于动态规划原理和李代数理论，得到了相应的HJB方程及值函数基于李对称的解析表达式，给出了最优投资策略，并通过待定系数法验证了结果的正确性。

We build a market model , import utility functions , and compare the conditions of utility maximization in order to find the regions of different investor s optimal strategy , using the Hamilton-Jacobi-Bellman equation ( HJB equation ) .

本文通过建立市场模型、投资者预算约束条件系统，采用HARA效用函数，利用效用最大化条件，和随机参数控制问题求解最优的方法，得出期权定价方程和不同交易条件下投资者最优投资组合策略。

In this Part , using the optimal control of the stochastic control theory , we set up the HJB function of this kind of risk model . We can obtain the optimal strategy of investment in order to make the ruin Probability being least .

在这一部分，主要应用了随机控制理论中的最优控制方法，建立了该模型的HJB方程，从而可以进一步找到该模型的最优投资策略，使得破产概率最小化。

Methods adopted in this dissertation are the dynamic programming principle and the stochastic analysis theory , through which the HJB equation corresponding to the control question can be worked out , and therefore , the optimal strategy with feedback from can be obtained .

第三章在第二章讨论的基础上考虑借贷利率不同时的情况，利用动态规划原理与随机分析方法，最优策略可以通过控制问题对应的HJB方程求得。

A new type of hydro - hybrid journal bearing meeting the requirement of superhigh speed and high power has been developed . The structure , theoretical analysis and numerical calculation of SS - HP HJB are presented in detail in this paper .

本文介绍了一种适于超高速大功率工况的新型液体动静压混合轴承（简称SS－HPHJB），详细介绍了SS－HPHJB的结构形式、理论分析及数值计算。

In chapter III and IV , the twi kind of risk-free interest rates are studied , respectively . By solving the objective function corresponding HJB equation , explicit expressions for the optimal investment strategy and the optimal value function are obtained .

本文第三章和第四章分别对两种无风险利率单独进行研究，通过求解目标函数所对应的HJB方程得到最优投资策略和最优值函数的明确表达式。

The simple portfolio investment model is given , with the HJB equation . The optimal portfolio investment problem is discussed under some given supposition , the quantitative relations are gotten between the investment strategies and riskless investment income rate and risk investment income rate are gotten .

建立简单的衍生证券投资组合模型，利用HJB方程，讨论了在一定假设条件下衍生证券最优投资问题，得到相关投资策略与无风险投资收益率及风险投资期望收益率之间定量关系。

Secondly , suppose that the price processes of the risky stock satisfy Markov-modulated geometric Brownian motion . We get the explicit expressions of the optimal portfolio strategies and the optimal value functions for the exponential utility functions by applying the dynamical programming principle ( HJB equations ) .

然后，在风险股票价格过程服从马氏调制的几何布朗运动的条件下，应用动态规划原理（HJB方程）得到了该非零和随机微分投资博弈问题的显式解。