【作者】 闫伟；

【导师】 李树荣；

【作者基本信息】 中国石油大学 ， 化学工程与技术， 2008， 博士

【摘要】 本文主要针对石油期货市场,建立了带有汇率波动因素的石油期货的价格模型,然后研究了基于随机最优控制理论的投资组合方案。对于实际的石油期货市场,在标的资产的即时价格、便利收益和利率的基础上加入了汇率的因素,建立了一个四因子的石油期货预测模型,而且所采用的模型是一个不连续的价格过程。推导出期货价格过程所满足的偏微分方程,并且求解出终端时刻边界条件下的带有参数的偏微分方程的通解,然后运用历史数据,采用加权最小二乘的方法辨识参数。针对风险度量的原则,下半方差更能反映投资者的愿望,因此用半方差取代方差来衡量风险,并将单阶段半方差投资组合模型推广到多阶段的情况,提出了一个多阶段半方差的投资组合模型。针对这一模型的目标函数在某些点不可导的特点,提出了一种基于粒子群位移转移思想的混合遗传算法。针对连续时间的投资组合方式,讨论了带有跳跃扩散过程和禁止卖空的条件下的在一般的连续时间均值-方差的模型,利用随机线性二次型的控制理论和方法,将其转化为随机哈密顿-雅克比-贝尔曼方程,推导出了投资的有效边界。在加入汇率因素后,讨论了一类随机最优投资情况及其投资策略。又针对安全首要的投资原则,求出了在连续时间跳跃扩散情况下的投资组合中的最优投资策略。当加入VaR约束之后,讨论了它对一般连续时间均值-方差投资模型的投资策略的影响。对于投资受到约束的情况,相对应的带有约束的HJB方程比较难求解出精确解。针对一类连续时间均值-方差的投资组合模型,分别提出了一种带有线性约束和非线性约束的数值求解方法。最后为了说明上述模型和方法的有效性,选择了英国伦敦期货市场的布伦特原油期货和中国上海期货市场的燃料油期货的实际例子。首先运用历史的数据分别辨识了四因子期货模型通解的参数。然后,分别建立了基于半方差目标函数和连续时间均值方差投资组合原则的随机最优投资组合模型,利用前面所述的计算方法分别求出相对应的最优投资策略。更多还原

【Abstract】 This dissertation investgates the modeling of petroleum futures price with exchange rate volatility and optimal portfolio solving based on stochastic optimal control theory. The contributions are mainly presented as follows.For petroleum futures market, a four-factor futures price model with the underling asset, convenience yield, instantaneous risk free interest rate and exchange rate volatility, is proposed. The corresponding partial differential equation(PDE) with terminal boundary condition of the model is drawn. The general solution with parameters of the above PDE is derived. The parameters are estimated by using the weight least squares approach with historical data for special cases.For objective of risk sssessment, downside risk has impacted on the practitioner’s view of risk apparently. Variance is substituted by semi-variance in Markowitz’s portfolio selection model. Moreover, one period portfolio selection is extended to multi-period. A class of multi-period semi-variance model is formulated. In the model, the objective function is nonsmooth in some points. So many methods of optimization, which depend on gradient information, cannot solve the problem. Therefore, a hybrid genetic algorithm (GA), which makes use of the position displacement strategy of the particle swarm optimizer (PSO) as a mutation operation, is applied to solve the multi-period semi-variance model.For continuous-time investment problem, the mean-variance(M-V) portfolio model based on discontinuous prices which they follow jump-diffusion processes, is established. Meanwhile, the short-selling of risky assets is prohibited. After presenting the corresponding stochastic Hamilton-Jacobi-Bellman(HJB) equation of the problem, the solution of the HJB equation based on stochastic linear-quadratic(LQ) control theory is derived. The exchange rate is considered in a class of optimal M-V model. The efficient frontier and optimal strategies are also provided. Besides, the optimal strategies are also derived under the safety-first criterion. Moreover, the effects on efficient frontier under a Value-at-Risk(VaR) constraint are illustrated in the M-V model.For some strategies which are restricted in the process of investment, the exact solution of corresponding stochastic HJB equation with linear and nonlinear constraints can not be obtained. Therefore, a kind of numerical algorithm based on iterative method is proposed to find the optimal solution.In order to demonstrate the effectiveness of the theoretical models and numerical methods, the Brent crude oil futures in London exchange market and the fuel futures in Shanghai exchange market are selected to be examples. With the help of historical data of the above two markets, the parameters of general solution with regard to the four-factor futures model are estimated. Then, the stochastic optimal control models based on the semi-variance as the objective function and continuous time mean-variance criterion, are established respectively. The optimal strategies are obtained by using numerical approaches.更多还原