Petroleum Futures Price Modeling Under Exchange Rate Volatility And Stochastic Optimal Portfolio Solving

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.