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假设金融市场中存在一种无风险资产和多种风险资产,且无风险利率是动态变化的,是服从Vasicek利率模型的随机过程。应用Legendre变换和动态规划原理对效用最大化下的最优投资策略进行了研究,得到了幂效用和指数效用下最优投资策略的显示解。算例分析了参数变动对最优投资策略的影响。
Assuming there is a risk-free asset and a variety of risk assets in the financial market, and the risk-free interest rate is dynamic, it is a stochastic process subject to the Vasicek interest rate model. By using Legendre transformation and dynamic programming principle, the optimal investment strategy under the maximization of utility is researched, and the display solution of the optimal investment strategy under the exponential utility and power efficiency is obtained. The example analyzes the influence of parameter variation on the optimal investment strategy.