Optimal portfolios in stochastic finance

许多复杂的动态系统可以用随机微分方程成功地建模，特别是股票市场。在金融市场中，投资者可能会寻求建立一种动态策略，使他能够优化预期终端财富的某个函数。考虑到这一点，他必须根据不断更新的信息流做出决策，而不能准确预测未来的市场波动。

Many complex dynamic systems ared modeled successfully by stochastic differential equations and this is particulary the case for stock markets. In a financial market, an investor might seek to establish a dynamic strategy allowing him to optimize a certain function of the expected terminal wealth. With this in mind, he must base his decisions on a continuously updated flow of information without being able to exactly predict future market fluctuations.