## Merton Lecture: A Good Fit for SIAM

**September 15, 1998**

Former SIAM managing director I.E. Block, in whose honor SIAM's annual community lectures are named, found Robert Merton's Toronto lecture a perfect fit with the goals of the founders of SIAM. Never one to sit back in idle contemplation of the past, Block (himself one of the founders) thinks about ways in which SIAM could put Mer-ton's message to work today.

Robert C. Merton's I.E. Block Community Lecture, given in July at SIAM's annual meeting in Toronto, was a superb example of the vision SIAM's founders had for the new society on its creation in early 1952. Merton, who with Myron C. Scholes received the Nobel memorial prize in economics in 1997, described how the use of mathematically complex models has become common in the relatively young finance industry, and how these models have led to greater understanding of new financial practices and products. Fostering the use of sophisticated mathematics to address real-world problems, especially in commerce and industry, was the underlying motivation for the creation of SIAM.

Merton provided a splendid overview of the role of mathematics in the evolution of the financial industry since the late 1960s, when the financial models developed in academe were becoming considerably more sophisticated. These "new models of dynamic portfolio theory, intertemporal capital asset pricing, and derivative-security pricing," he said, "employed stochastic differential and integral equations, stochastic dynamic programming, and partial differential equations." (For details on the lecture, see James Case's report on page 1 in this issue of *SIAM News*.)

In 1973, with Myron Scholes and Fisher Black (who died in 1995), Merton developed the now well known Black-Scholes model for option pricing. (It was for this work that he and Scholes shared the Nobel prize.) "In the time since publication of our early work on the option-pricing model, Merton told the audience in Toronto,

"the mathematically complex models of finance theory have had a direct and wide-ranging influence on finance practice. This conjoining of intrinsic intellectual interest with extrinsic application is central to research in modern finance. The combining of academic finance research and financial practice has been a central theme of my professional life."

For the future, Merton said that "financial-engineering creativity," and the technology and transactional databases needed to implement that creativity reliably and cost-effectively, "are likely to become central competitive elements of the industry." Neither one, he feels, can be achieved without greater reliance on mathematical modeling. He predicts that mathematical models and the supporting computational technologies will play an indispensable role in the functioning of the global financial system.

* * *

Surely the impact mathematics and economics have had on financial practice is the result of interactions and collaborations among mathematicians, economists, and practitioners of finance. Similar collaborations have occurred in other industries-the aircraft, aerospace, chemical, communication, and computer (hardware and software) industries, among many others-in which there are products, processes, and/or applied research. SIAM has been effective in supporting the applied and computational mathematics done in most of these industries, but it should be doing more to foster interactions and collaborations among applied/computational mathematicians and practicing engineers and scientists, especially in industrial environments.

In my view, the next step for SIAM is to fully comprehend how mathematics (applied and computational) is being used in industry by the practitioners of mathematics and how that use might be enhanced. The number of PhD mathematicians practicing in industry is relatively small. Perhaps there simply is no payoff for industry in employing more mathematicians. On the other hand, many engineers, scientists, and other practitioners in industry are designing products and processes, analyzing the behavior of structures and systems, modeling generally, and doing other things that require the use of mathematical methods and software. How do they learn to use these methods? How do they know when the traditional methods will fail and new ones are needed? What are the mechanisms for enhancing the use of traditional methods and for signaling the need for new ones? How can mathematicians find out about emerging engineering and scientific problems so that they can anticipate the needs for new research and development? How do technology transfers take place? What new roles are there for suitably trained mathematicians?

SIAM has an ongoing project, Mathematics in Industry, which was initiated in 1993. The first phase of this project culminated in the publication of a survey in 1995. The survey provided answers to some of these (and other) questions, but there is more to be learned. The project is continuing---a second phase consisting of a series of university-industry workshops on the use of mathematics in industry is under way now (see page 1 of this issue for a report on the first of the workshops). Undoubtedly, additional understanding will result from this phase of the project.

SIAM also has conducted extensive discussions on the possibilities for a "professional master's degree" curriculum in applied mathematics that could qualify students for mathematical work in industry. Recently, SIAM's education committee developed a prospectus for such a program. Why not extend the effort to a "professional PhD degree," with the goal of training mathematically skilled workers for industry at the PhD level?

These projects could be used to jump-start a program that would prepare students for modeling, problem-solving, and consulting positions in industry. Perhaps there are some ideas to be gleaned from Merton and his presentation. Merton has an undergraduate degree in engineering mathematics, a master's degree in applied mathematics, a PhD in economics, and great skill as a communicator. Perhaps students with similar educational backgrounds, and PhD-level degrees in an area of engineering or science, could carry to industry not only the engineering/scientific image traditionally accepted by industry but also substantially enhanced mathematical and computational skills and problem-solving ability. The education of those students would be a way to inject more mathematical and computational skills into the industrial enterprise.

Such a graduate curriculum could be defined, developed, and evaluated by SIAM, with the goal of identifying and testing opportunities for a new breed of MS- and PhD-level students who could contribute well to industrial enterprises. Subsequently, SIAM could promote the acceptance and development of the program by the universities and, in time, develop a certification program for this new breed of graduates, who would require periodic continuing education to remain certified. Such a program could broaden the market for mathematically trained students and strengthen the role of mathematics departments in interdisciplinary education. The idea is consistent with the National Science Foundation's interdisciplinary program, Mathematics and its Applications Throughout the Curriculum, under which mathematics departments are collaborating with other university departments to develop interdisciplinary teaching materials.

How about establishing a special high-level SIAM committee, with well-defined goals, to develop and carry out such a program?

*I. Edward Block is managing director emeritus of SIAM.*