Approximation theory and asymptotic methods form a foundational framework that bridges classical ideas with modern numerical analysis, enabling researchers to obtain practical, near‐optimal solutions ...

SIAM Journal on Applied Mathematics, Vol. 50, No. 6 (Dec., 1990), pp. 1517-1532 (16 pages) An approximation method of Moore for Kelvin-Helmotz instability is formulated as a general method for ...

Clinical trials have traditionally followed a fixed design, in which patient allocation to treatments is fixed throughout the trial and specified in the protocol. The primary goal of this static ...

In this talk we present few instances of multilevel approximation methods involving PDEs with random parameters and associated scalar output quantities of interest (QoI). Multilevel methods aim at ...

The stochastic root-finding problem is that of finding a zero of a vector-valued function known only through a stochastic simulation. The simulation-optimization problem is that of locating a ...

A critical issue in the credit risk industry is the accurate, efficient and robust pricing of collateralized debt obligations (CDOs) in a variety of mathematical models. These and many similar basket ...

Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods, and ...

In their 2001 paper, Longstaff and Schwartz suggested a method for American option pricing using simulation and regression, and since then this method has rapidly gained importance. However, the idea ...