The mathematics of finance involves a wide spectrum of techniques that go beyond traditional applied mathematics. The field has witnessed a tremendous amount of progress in recent years, which has inspired communication and networking among researchers in finance, economics, engineering, and industry. This volume contains papers based on talks given at the first AMS-IMS-SIAM Joint Summer Research Conference on Mathematics of Finance held at Snowbird (UT). Topics covered here include modeling, estimation, optimization, control, risk assessment and management, contingent claim pricing, dynamic hedging, and financial derivative design. The book is suitable for graduate students and research mathematicians interested in mathematical finance.