风险函数

The main research results in this dissertation can be given as following:Firstly, the bidding strategies and affections of generation companies on the TOU power price are analyzed; Supply function model is employed to simulate the bidding strategies of generation companies in power pool. Some meaningful results are obtained through the proposed equilibrium equations model, when different bidding parameters are selected to maximize profit of suppliers, such as the the numeral of generation company, the block bidding, and power demand elasticity. Based on these results, the affections between the bidding strategies and the TOU power price are discussed.Secondly, the important principles consider the factor of bidding strategies of generation companies and consumers gaming strategies are proposed to constitute the new TOU power price model under present electricity market. Based on these pricinples a new mathematical model of TOU power price is constructed, to evade electricity market risk, partition the peak-valley, ascertain the consumers' response curve, and protect the ambilateral profits.Thirdly, the affections of the TOU power price strategies for reducing the network loss, adjusting node voltage, improving load curve of power system, and protecting the consumers' benefits in electricity market are analyzed with applications of a city real time load data of Jiangsu province.

针对"厂网分开，竞价上网"的电力市场运营模式，本文主要完成了以下研究工作：1研究了发电商不同的竞价上网策略，利用供给函数均衡方法，建立了发电商的竞价上网策略模型，给出了市场均衡解的具体解法；讨论了不同条件下发电商的竞价策略对市场的影响，并获得了发电商的最优上网竞价策略，明确了竞价上网与峰谷分时电价之间的影响因素；利用电力系统负荷曲线，建立了发电商最优竞价策略与峰谷分时电价之间的相互联系，通过仿真算例分析了峰谷分时电价与发电商最优报价之间的相互影响。2提出了"厂网分开，竞价上网"电力市场模式下，考虑发电侧竞价和用户侧博弈等风险因素影响，峰谷分时电价理论建模在规避电网企业运营风险，保护供电方与用户双方的利益、确定用户响应曲线、划分峰谷时段、设置合理的电价拉开比等方面所应遵循的基本原则，在此基础上建立了适合电力市场模式的峰谷分时电价模型。3从原理上分析了需求侧实行峰谷分时电价策略，对削峰填谷，提高负荷率，改善负荷曲线形状，降低电力系统的电能损耗和电压损耗等方面的影响，并进行了仿真验证。

However, on the basis of the commission and agency theory, the agency problems become more and more serious due to the different goals between owner and manager, and the information dissymmetry.

而根据委托代理理论，由于所有者与经营者的目标函数不同，信息的不对称，风险偏好以及道德风险的存在，使得企业中的代理问题日益突出。

The Mean-CVaR (Conditional Value-at-Risk) portfolio optimization model is proposed to calculate a globally optimal portfolio under concave transaction costs. A non-decreasing concave function is employed to approximate origin transaction costs function.

研究了当投资组合的风险用条件风险价值（Conditional Value at Risk，简称CVaR）度量，考虑凹交易费用的投资组合选择问题，通过对交易费用采用非线性的凹函数，建立了一个均值-CVaR模型。

Thirdly, the problems of institution investor'optimal liquidation strategy and optimal liquidation time were investigated with the conditions that the price of risky asset followed arithmetic Brown motion and liquidation velocity was limited. The problems involved the following scenes: price impact function was linear expression of liquidation velocity which was boundary closed set with an isolated point; price impact function was stochastic; price impact function was nonlinear.

接着，当风险资产的价格服从算术布朗运动，且对投资者的变现速度做出限制时，研究机构投资者的最优变现策略和最优变现时间问题，其中包括：价格冲击函数为变现速度的线性函数，变现速度是一带有孤立点的有界闭集；价格冲击是随机形式；价格冲击是变现速度的非线性函数。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

At first, draws the atomic seeps into executing probabilistic matrix and transferring probabilistic matrix. Change LEG for probability logic seeps through picture of probabilistic logical exploitation graph PLEG, then explains the PLEG problem to the solution of MDP value function and optimal policy.

本文提出了一种基于MDP的风险概率计算模型PLEG-MDP，首先通过引入原子渗透执行概率矩阵和转移概率矩阵，将LEG转换为概率逻辑渗透图PLEG，然后将PLEG解释为MDP，进而求解MDP问题的价值函数和最优策略，其分别对应着目标网络的最大风险概率和风险路径。

In this paper, we use approximate distribution comes from probability generating function in estimating credit VaR. Further, we perform the credit VaR sensitive analysis for multi-sector factors based on different sector correlation assumption.

本文在信用风险加成模型之下，利用机率产生函数的近似分配计算信用风险值，并在多个部门因子中，在不同相关性部门因子分配假设下，比较信用风险值之敏感度分析。

A standard expected value model for multi-objective multi-stage transmission planning is presented to realize the transmission optimal planning with the control of line overloading risks. In this model, a constraint of overloading risks is built with expected value and standard deviation of random line active power and two objectives are given as expected value of the average power loss and discount value of the investment cost. By modeling uncertain informations with probability theory, the probabilistic DC power flow is adopted for the correlated calculations among random variables in the planning model.4 A novel multi-objective transmission planning approach that considers transmission investment profit is proposed. Requests for transmission investment profit and social welfare are involved in the proposed planning approach.

以方案总投资费用贴现值和平均网损期望值为目标函数，建立多目标多阶段输电网规划的期望值模型，以线路有功潮流过负荷随机变量的期望值和标准差构建过负荷风险约束，考虑了风险发生概率和严重程度两方面的特征，通过对不确定性信息的概率建模，利用概率直流潮流进行各随机变量的相关计算，实现了控制过负荷风险条件下的输电网优化规划。4提出考虑输电投资收益的多目标输电网规划方法，综合考虑市场参与者对输电投资收益和社会总福利的要求加热管及其对输电网规划的影响。

Because constructing the fuzzy function is aim at every target of financial risk dividedly, the fuzzy function constructed has target and is a quantitative member belongs to [0,1]. Thus the constructing of function has more objective, and better reflect the unified target .

因为构造出的模糊函数是分别针对金融风险的每一个目标的，这样构造出的模糊函数带有目标性，且是[0，1]区间的一个量化数，这样函数的构造就比较有针对性，且更好地反映了目标化的统一。

This paper presents the portfolio selection problem of two-attribute money and creates a model of portfolio selection based on two-attribute money, which can both contain the existing portfolio models and overcome the above-mentioned deficiencies. A series of new concepts is put forward, such as, holding wealth, obtainable wealth, short-term utility function, short-term expectation-variance utility function, state-expectation-variance utility function, short-term expectation-variance utility curve, long-term expectation-variance utility curve, margin utility contribution force, additional contribution force, profit-risk exchange rate and optimal portfolio expansion curve; The state-expectation-variance analytical method is developed from the expectation-variance analytical method; A set of systematic theories concerning two-attribute portfolio selection is thus established.

本文提出了两属性货币的证券组合选择问题；创建了既能包含现有证券组合选择模型又能克服上述两点不足的两属性证券组合选择模型；提出了持有财富、可获财富，短期效用函数，短期期望—方差效用函数、状态—期望—方差效用函数，短期期望—方差效用曲线、长期期望—方差效用曲线，边际效用贡献力，附加贡献力，收益—风险替换率，最优证券组合扩展线等一系列新概念；把期望—方差分析方法发展成状态—期望—方差分析方法；建立了两属性证券组合选择模型的一套系统的理论。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。