The paper examines the optimal behavior of a single dealer who is faced with a stochastic demand to trade (modeled by a continuous time Poisson jump process) and facing return risk on his stock and on the rest of his portfolio (modeled by diffusion processes). Using stochastic dynamic programming, we derive the optimal bid and ask prices that maximize the dealer's expected utility of terminal wealth as a function of the state in which he finds himself. The relationship of the bid and ask prices to inventory of the dealer, instantaneous variance of return, stochastic arrival of transactions and other variables is examined.

ABSTRACT Most models of bank failure have assumed that the path towards bankruptcy or insolvency is smooth and continuous. As a consequence a number of early‐warning systems have been suggested in the banking and financial literature to aid regulators in the identification of potential problem banks. However, these systems may be of little use when the path towards failure is explosive, involving a sudden crash or catastrophe. This paper seeks to examine such cases by applying the theory of catastrophes to bank failure. A model is developed to show how the interaction between bank management, regulators and depositors can induce catastrophic failure. It is argued that there is a crucial relationship between the power of regulatory intervention and depositors confidence levels which is both necessary and sufficient for catastrophe to occur. It is also argued that catastrophe appears to be more likely for large money market banks rather than small banks. Finally, some suggestions are made for regulatory policy and for further research in the area.

Most models of bank failure have assumed that the path towards bankruptcy or insolvency is smooth and continuous. As a consequence a number of early-warning systems have been suggested in the banking and financial literature to aid regulators in the identification of potential problem banks. However, these systems may be of little use when the path towards failure is explosive, involving a sudden crash or catastrophe. This paper seeks to examine such cases by applying the theory of catastrophes to bank failure. A model is developed to show how the interaction between bank management, regulators and depositors can induce catastrophic failure. It is argued that there is a crucial relationship between the power of regulatory intervention and depositors confidence levels which is both necessary and sufficient for catastrophe to occur. It is also argued that catastrophe appears to be more likely for large money market banks rather than small banks. Finally, some suggestions are made for regulatory policy and for further research in the area.