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Three essays on stochastic optimization applied in financial engineering and inventory managment.

机译：三篇关于随机优化的文章在金融工程和库存管理中的应用。

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摘要

Stochastic optimization methods are now being widely used in a multitude of applications. This dissertation includes three essays on applying stochastic optimization methods to solve problems in inventory management and financial engineering.; Essay one addresses the problem of simultaneous price determination and inventory management. Demand depends explicitly on the product price p, and the inventory control system operates under a periodic review (s, S) ordering policy. To minimize the long-run average loss, we derive sample path derivatives that can be used in a gradient-based algorithm for determining the optimal values of the three parameters (s, S, p) in a simulation-based optimization procedure. Numerical results for several optimization examples via different stochastic algorithms are presented, and consistency proofs for the estimators are provided.; Essay two considers the application of stochastic optimization methods to American-style option pricing. We apply a randomized optimization algorithm called Model Reference Adaptive Search (MRAS) to pricing American-style options through parameterizing the early exercise boundary. Numerical results are provided for pricing American-style call and put options written on underlying assets following geometric Brownian motion and Merton jump-diffusion processes. We also price American-style Asian options written on underlying assets following geometric Brownian motion. The results from the MRAS algorithm are compared with the cross-entropy (CE) method, and MRAS is found to be an efficient method.; Essay three addresses the problem of finding the optimal importance sampling measure when simulating portfolios of credit risky assets. We apply a gradient-based stochastic approximation method to find the parameters in the minimum variance problem when importance sampling is used. The gradient estimator is obtained under the original measure. We also employ the CE method to solve the same variance minimization problem. Numerical results illustrating the variance reduction are presented for the estimation of the portfolios' expected loss, unexpected loss and quantiles.
机译：随机优化方法现已广泛应用于众多应用中。本文包括三篇关于运用随机优化方法解决库存管理和财务工程问题的论文。一篇文章讨论了同时确定价格和库存管理的问题。需求明确取决于产品价格p，并且库存控制系统在定期检查（s，S）的订购策略下运行。为了使长期平均损失最小化，我们导出了样本路径导数，该样本路径导数可用于基于梯度的算法中，以便在基于仿真的优化过程中确定三个参数（s，S，p）的最佳值。通过不同的随机算法给出了几个优化实例的数值结果，并为估计量提供了一致性证明。论文二考虑了随机优化方法在美式期权定价中的应用。我们通过参数化早期运动边界，将一种称为模型参考自适应搜索（MRAS）的随机优化算法应用于美式期权定价。提供了数值结果，用于按照几何布朗运动和默顿跳跃扩散过程对标的资产上的美式看涨期权和看跌期权进行定价。我们还按照布朗运动后的基础资产对美式亚洲期权定价。将MRAS算法的结果与交叉熵（CE）方法进行比较，发现MRAS是一种有效的方法。论文三解决了在模拟信贷风险资产组合时寻找最佳重要性抽样方法的问题。当使用重要性抽样时，我们应用基于梯度的随机逼近方法来找到最小方差问题中的参数。梯度估计器是在原始量度下获得的。我们还采用CE方法来解决相同的方差最小化问题。给出了说明方差减少的数值结果，用于估计投资组合的预期损失，意外损失和分位数。

著录项

  • 作者

    Zhang, Huiju.;

  • 作者单位

    University of Maryland, College Park.$bBusiness and Management: Decision & Information Technologies.;

  • 授予单位 University of Maryland, College Park.$bBusiness and Management: Decision & Information Technologies.;
  • 学科 Business Administration Management.; Business Administration Banking.; Operations Research.
  • 学位 Ph.D.
  • 年度 2007
  • 页码 129 p.
  • 总页数 129
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 贸易经济;金融、银行;运筹学;
  • 关键词

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