Mathematical Sciences: Brownian Motion Models of Financial Markets

主要的研究人员将研究一些问题， 模拟金融市场。 这项工作将包括特遣队 索赔定价，效用最大化和均衡存在， 证券市场的特征表现出各种 不完整性。 证券被模拟为Ito 流程. 这些模型中的不完整性可能会出现， 证券太少，无法对冲所有相关风险， 与潜在的布朗运动，因为有 对可接受的投资组合的限制，如卖空 或者是因为交易成本。 的问题 借贷和投资的不同利率也将 考察

The principal investigators will work on some problems in modeling financial markets. The work will include contingent claim pricing, utility maximization and equilibrium existence and characterization in securities markets which exhibit various kinds of incompleteness. Securities are modelled as Ito processes. Incompleteness in these models can arise because there are too few securities to hedge all the risk associated with the underlying Brownian motion, because there are constraints on admissible portfolios such as short-selling prohibition, or because of transaction costs. The problem with different interest rates for borrowing and investing will also be examined.