JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS November 1975 THEORY OF FINANCE FROM THE PERSPECTIVE OF CONTINUOUS TIME

It is not uncommon on occasions such as this to talk about the shortcomings in the theory of Finance, and to emphasize how little progress has been made in answering the basic questions in Finance, despite enormous research efforts. Indeed, it is not uncommon on such occasions to attack our basic "mythodology," particularly the "Ivory Tower" nature of our assumptions, as the major reasons for our lack of progress. Like a Sunday morning sermon, such talks serve many useful functions. For one, they serve to deflate our professional egos. For another, they serve to remind us that the importance of a contribution as judged by our professional peers (the gold we really work for) is often not closely aligned with its operational importance in the outside world. Also, such talks serve to comfort those just entering the field, by letting them know that there is much left to do because so little has been done. While such talks are not uncommon, this is not what my talk is about. Rather, my discussion centers on the positive progress made in the development of a theory of Finance using the continuous-time mode of analysis. Hearing this in .1975, amidst an economic recession with a baffling new disease called "stagflation" and with our financial markets only beginning to recover from the worst turmoil in almost 40 years, some will say that I am embarked on a fool's errand. Perhaps. At any rate, on this errand, I shall discuss the continuous-time solutions to some of the basic problems of Finance: portfolio selection, capital market equilibrium, and the pricing of capital assets; the derived functions of financial intermediaries and instruments; and the pricing of corporate liabilities. Rather than dwelling on the technical aspects of obtaining these solutions, I will discuss the substantive results and why they seem to differ from those obtained in other modes of analysis. While my main interest is in the substantive results, some methodol<$gical discussion is necessary because the continuoustime mode is relatively new. However, I will attempt to keep this discussion to a minimum by emphasizing only those assumptions that differ from its discrete-time counterpart, and leave those assumptions common to both types of analysis as understood.