Solving option pricing problems numerical methods form an essential part. This paper discusses five numerical methods: Black-Scholes-Merton, Monte Carlo, Binomial, Trinomial, and Finite Difference. A comparison of these methods for both European and American put options shows a graphical...

Self-propelled jumping of two polymeric droplets on superhydrophobic surfaces is investigated by three-dimensional direct numerical simulations. Two identical droplets of a viscoelastic fluid slide, meet and coalesce on a surface with contact angle 180 degrees. The droplets are modelled by the...

To investigate the coupled conduction-radiation heat transfer in C/SiC composites, a multiscale numerical method is proposed in this paper. The multiscale method combines a three-scale physical model and a multiscale mathematical method for predicting the thermal conductivity of composite...

This paper presents and compares Newton-based methods from the applied mathematics literature for solving the matrix quadratic that underlies the recursive solution of linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and...

The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs) was originally formulated using Euler time discretizations and a uniform space grid. In this paper, we utilize a tree-like spatial discretization that approximates the BSDE on the...

This paper studies dynamic programming for quantile preference models, in which the agent maximizes the stream of the future τ-quantile utilities, for τ ∈ (0,1). We suggest numerical methods, based on value function iterations, for solving the quantile recursive dynamic programming, and...