Stochastic control in finance and economics

金融和经济中的随机控制

• 批准号: 8051-2007
• 负责人: Haussmann, Ulrich
• 金额: $ 0.66万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=361986
• 关键词: Stochastic; control; finance; economics

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?

经济均衡是自由市场经济的隐含假设：存在价格、利率等（宏观经济变量），如果每个个人和公司都按照自己的最佳利益行事，那么资源就会得到分配，商品就会有效生产。在这个项目中，建立了随机环境下经济的数学模型。每个人都有很多决定要做：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中，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。如果个人偏好取决于随机机制，例如，在牛市中，我们可能希望财富最大化，但在熊市中，我们关心的是财富保值，那么应该如何选择资产组合？