Optimal Consumption-Investment Problems in Incomplete Markets with Stochastic Coefficients
Optimal Consumption-Investment Problems in Incomplete Markets with Stochastic Coefficients
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DOI：
10.1137/s0363012904440885
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发表时间：
2005-10
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通讯作者：
Netzahualcóyotl Castañeda-Leyva;D. Hernández-Hernández-D.-Hernández-Hernández-83203043
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作者：
Netzahualcóyotl Castañeda-Leyva;D. Hernández-Hernández-D.-Hernández-Hernández-83203043
本文的目的是解决不完全金融市场背景下的最优消费-投资问题。该模型是Black和Scholes扩散模型的推广，在该模型中，模拟股票价格的扩散系数取决于一些随机的经济因素。在此基础上，给出了一种求最优解的基本方法。将该方法与随机控制技术相结合，得到了Hara效用函数和对数效用函数的显式解。
The goal of this paper is to solve an optimal consumption-investment problem in the context of an incomplete financial market. The model is a generalization of the Black and Scholes diffusion model, where the coefficients of the diffusion modelling the stock's price depend on some stochastic economic factors. Based on the martingale approach, a basic methodology to get the optimal solution is presented. Combining this procedure with stochastic control techniques, explicit solutions for HARA and logarithmic utility functions are obtained.