Mathematical Sciences: Applications of Stochastic Control toConsumption/Investment Decisions, Equilibrium Analysis and Production

该项目包括建议在三个分领域进行的研究， 其中前两者是紧密相连的，而后者是 稍微不相交。 在第一个领域，一般的问题是， 不断投资或消费，以便获得净收益 总消耗是最大值。 投资可以分为 一个固定回报率的债券和几个风险较高的债券之间， 名的股票明细金额 借贷和卖空（投资）等变化 负量）是可能的。 在以前的一些工作中，作者 已经取得了一些进展的情况下，各种利率的 回报是随机的，而不是固定的。 在最近的一项工作中， 手段的措施变化的论点，他们有联系的最佳 消费率的反馈形式的功能逆 消费函数的导数。 作者提出 无限版本问题的扩展， 借贷和卖空受到限制， 涉及破产支付。 第二个领域与第一个领域密切相关， 众多的代理人都在各自追求 最优消费和投资政策。 目标是 调查净投资的均衡情况，以及 财富创造都是零等，并显示存在现货 价格 最后一个领域，与上述交易略有脱节 在生产n的制造系统中， 在M机器上的商品。 目标是尽量减少持有 库存成本和生产系统，以满足特定的 即使在机器容易出现故障的情况下，也要满足这些要求。 作者 建议调查失败率为 与机器使用率成正比。 他们还建议延长 那里有一个连续的机器，但这似乎不太 说服力 这种类型的研究对经济理论和 股票管理，而在同一时间的主流， 目前的研究工作在控制视为数学的一部分。

This project consists of research suggested in three sub-areas, of which the first two are closely linked, while the last is slightly disjoint. In the first area, the general problem is one where money has to be continuously invested or consumed so that the net benefit of the total consumption is a maximum. The investments can be divided between a bond, with a fixed rate of return, and several risky stocks. Variations such as borrowing and short selling (investing negative amounts) are possible. In some previous work the authors have made some progress on the case where the various rates of return are random rather than fixed. Also in a recent work, by means of measure change argument, they have linked the optimal consumption rate in feedback form to the functional inverse of the derivative of the consumption function. The authors propose extensions in infinite versions of the problem, situations where borrowing and short selling are restricted, and cases where a bankruptcy payment is involved. The second area, which is closely related to the first, deals with a multiplicity of agents all pursuing their individually optimal consumption and investment policies. The goal is to investigate the equilibrium situation where net investment, and creation of wealth are all zero etc. and show the existence of spot prices. The last area, which is slightly disjoint from the above deals with the control of production in a manufacturing system producing n commodities on m machines. The goal is to minimize holding inventory costs and production systems so as to meet specified demands, even when machines are liable to failure. The authors propose to investigate the case where the failure rate is proportional to machine utilization. They also suggest an extension where there is a continuum of machines, but this appears less convincing. The research of this type is of interest to economic theory and stock management, while at the same time being in the mainstream of current research efforts in control seen as part of mathematics.