Stochastic filtering: Theory and applications in finance

The subject of this dissertation is stochastic filtering theory and its application to finance. The first chapter introduces the subject by working through a simple example and discussing the history of filtering theory. The second chapter derives the filtering equations for a multivariate continuous time framework, where the state and observation noise are correlated. This is accomplished using a technique presented in Krishnan (1984). The third chapter examines the problem of parameter estimation in a mixed continuous-discrete framework where the observable variables are comprised of both stocks and flows and the state and observation noise are correlated. This extends the work of Harvey and Stock (1985). The final chapter presents an application of stochastic filtering to the analysis of corporate capital structure.