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.
