不确定环境下的跳扩散连续时间资产配置策略

The strategy of jump-diffusion continuous-time asset allocation under uncertain environment

金融市场是一个复杂的非线性系统,在不确定环境下,如何在有限时域内最优配置资源,是金融理论研究的核心问题之一.面对现实生活中的大量不确定性因素以及多期投资问题,Markowitz的投资组合理论以及在其基础上发展起来的资本资产定价理论和套利定价理论则显得无能为力.本文研究了不确定环境下极大极小风险控制的连续时间投资组合优化问题,运用Bellman最优性原理和HJB方程构造了典型的资产组合优化模型,借助随机控制和多重网格数值逼近方法得到相应优化问题的最优投资策略,通过实证方法验证了过程风险控制下资产配置策略的有效性.

Financial market is a complex nonlinear system. In an uncertain environment, how to opti- mally allocate of resources in the limited time domain is one of the core problems of the financial theory research. It becomes helpless for Markowitz＇s portfolio theory, and capital asset pricing model （CAPM） and arbitrage pricing theory （APT） when facing with the large amount of uncertainties in real world. In this paper a continuous-time portfolio selection optimization decision is made with control on downside risk and minimax principle under uncertain environment, a typical portfolio selection model is established by use of Bellman principle of optimality and the HJB equation. We derive the optimal strategy with gen- eral stochastic control technique and numerical approximation algorithm for multi-grid computing. The effectiveness of the asset allocation strategy under process risk control is verified by empirical method in Chinese capital market.