This volume contains
papers, based on the invited talks given at the
AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences:
Mathematics of Finance, held in Snowbird, Utah, June
22-26, 2003.
This was the
first ever conference on mathematics of finance jointly sponsored by AMS, IMS,
and SIAM.
Financial mathematics is a rapidly expanding field. It involves a wide spectrum
of techniques that go far beyond the traditional applied mathematics. Research in
mathematics of finance has witnessed tremendous progress in recent years. The
Black-Scholes model and its various extensions for pricing of options have had an
influential impact on financial practice and led to a revolution in the financial in-
dustry. The introduction of stochastic analysis and stochastic control techniques
has resulted in a number of important advances. To name just a few, they include
the studies of valuation of contingent claims in complete and incomplete markets,
consumption-investment models with or without constraints, portfolio management
for institutional investors such as pension funds and banks, and risk assessment and
management using financial derivatives. These applications, on the other hand, re-
quire and stimulate many new and exciting theoretical discoveries. As a major
impetus to the development of financial management and economics, research in
mathematics of finance has had a major impact on the global economy. Moreover,
the development of mathematics of finance has created a large demand for mathe-
matics graduates at both Master and Ph.D. levels in the financial industry, resulting
in the introduction of this topic in the curriculum of mathematical sciences depart-
ments of many universities. The rapid progress has necessitated communication
and networking among researchers in different disciplines. This summer research
conference provided us with an excellent and timely opportunity. It brought to-
gether researchers from mathematical sciences, finance, economics, and engineering,
and financial industry to review and to update the recent advances, and to identify
future directions of mathematics of finance.
The scientific program of the conference consisted of 42 invited talks, a poster
session, and a panel discussion on research and education. While recent progress has
been surveyed, reviewed, and substantially updated, new ideas, models, methods,
and techniques have been explored. The invited speakers presented a broad spec-
trum of problems, models, and results involving modeling, estimation, optimiza-
tion, control, risk assessment and management, contingent claim pricing, dynamic
hedging, and financial derivative design. Valuation of contingent claims remains the
centerpiece of modern financial theory. Its key components include financial market
modeling and dynamic hedging. While the Black-Scholes models have been widely
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