Mathematical Sciences: Brownian Motion Models of Financial Markets

主要研究人员将研究金融市场建模中的一些问题。本文将包括或有债权定价、效用最大化和证券市场中表现出各种不完备性的均衡存在与表征。证券被建模为Ito过程。这些模型的不完全性可能会出现，因为有太少的证券无法对冲与潜在布朗运动相关的所有风险，因为对可接受的投资组合有限制，比如卖空禁令，或者因为交易成本。此外，还将研究借贷和投资利率不同的问题。

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.