This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European...

The problem of determining the unknown coefficient k=k(x) of the Sturm–Liouville operator Au≡−(k(x)u′(x))′+q(x)u(x) from the measured data at the boundary x=0;1 is considered. It is assumed that the function u=u(x) has several singular points in (0,1) of different types. As a result...

Effective risk management requires adequate risk measurement. A basic problem herein is the quantification of market risks: what is the overall effect on a portfolio if market rates change? First, a mathematical problem statement is given and the concept of `Maximum Loss' (ML) is introduced as a...

Effective risk management requires adequate risk measurement. A basic problem herein is the quantification of market risks: what is the overall effect on a portfolio if market rates change? First, a mathematical problem statement is given and the concept of `Maximum Loss' (ML) is introduced as a...