Chebyshev polynomial approximation to approximate partial differential equations

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 option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

On the real effects of financial pressure: Evidence from euro area firm-level employment during the recent financial crisis.

Using a large panel of unquoted euro-area firms over the period 2003-11, this paper examines the impact of financial pressure on firms’ employment. The analysis finds evidence that financial pressure negatively affects firms’ employment decisions. This effect is stronger during the 2007-2009 financial crisis, especially for firms in the periphery area compared to their counterparts in the core European economies. We also find that impact of financial pressure on employment is more potent for firms classified as financially constrained and operating in periphery economies during the financial crisis.