Stochastic control in finance and economics

经济均衡是自由市场经济背后的一个隐含的假设：存在价格、利率等(宏观经济变量)，如果每个人和公司都以自己的最佳利益行事，那么资源就会得到分配，商品就会得到有效生产。在这个项目中，建立了随机环境中经济的数学模型。个人需要做出多项决定：工作、消费、储蓄和投资。其目的是表明，即使在如此复杂的环境下，经济均衡也是存在的。另一个需要研究的问题是投资组合优化。如果个人偏好依赖于随机机制，那么应该如何选择资产组合？例如，在牛市中，我们可能想要最大化财富，但在熊市中，我们关心的是保存财富。

Economic equilibrium is an implicit assumption underlying free market economies: there exist prices, interest rates, etc. (macroeconomic variables) such that if every individual and corporation acts in their own best interest, then resources are allocated and goods are produced efficiently. In this project mathematical models of economies in a random environment are developed. The individuals have multiple decisions to make: how much to work, to consume, to save, to invest. The aim is to show that even in such complex settings economic equilibrium exists.Another problem to be investigated concerns portfolio optimization. How should a portfolio of assets be chosen if the personal preferences depend on a random regime, e.g. in a bull market we may want to maximize wealth, but in a bear market we are concerned with preserving wealth?