Free Boundary Problems in Mathematical Finance
Chadam's recent research efforts have been focused on the study of free boundary problems that arise in mathematical finance. With his colleague, Xinfu Chen, their students, and foreign collaborators, he has studied early exercise boundaries for American style options analytically and numerically. In addition to giving precise estimates for the location of these boundaries, the work provided the first rigorous proof of the existence and uniqueness of the solution to the mathematical problem for the American put in the nonlinear integral equation formulation as well as convexity of its early exercise boundary. These methods have been carried over in a unified manner to treat a wide range of similar problems, including inverse first crossing problems in credit default and optimal strategies for prepayment of mortgages. Present research in this area is directed toward the study of default contagion in the context of higher dimensional value-of-firm models and multiple boundaries in callable convertible bonds.
Chadam and his students also are interested in a variety of other problems, such as pricing and hedging equity-linked securities and calibrating jump-diffusion and stochastic volatility models to electricity prices and using them to price futures contracts and swing options.