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

The characteristics of the mean-variance, efficient portfolio frontier have been discussed at length in the literature. However, for more than three assets, the general approach has been to display qualitative results in terms of graphs. In this paper, the efficient portfolio frontiers are derived explicitly, and the characteristics claimed for these frontiers are verified. The most important implication derived from these characteristics, the separation theorem, is stated and proved in the context of a mutual fund theorem. It is shown that under certain conditions, the classic graphical technique for deriving the efficient portfolio frontier is incorrect.