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.

Export-market dynamics and the probability of firm closure: Evidence for the UK

This study presents the first empirical analysis of the determinants of firm closure in the UK with an emphasis on the role of export-market dynamics, using panel data for a nationally representative group of firms operating in all-market based sectors during 1997-2003. Our findings show that the probability of closure is (cet. par.) significantly lower for exporters, particularly those experiencing export-market entry and exit. Having controlled for other attributes associated with productivity (such as size and export status), the following factors are found to increase the firm’s survival prospects: higher capital intensity and TFP, foreign ownership, young age, displacement effects (through relatively high rates of entry of firms in each industry), and belonging to certain industries. Interestingly, increased import penetration (a proxy for lower trade costs) leads to a lower hazard rate for exporting entrants and continuous exporters, whilst inducing a higher hazard rate for domestic producers or those that quit exporting.

Second-Order Approximation to the Rotemberg Model around a Distorted Steady State

Less is known about social welfare objectives when it is costly to change prices, as in Rotemberg (1982), compared with Calvo-type models. We derive a quadratic approximate welfare function around a distorted steady state for the costly price adjustment model. We highlight the similarities and differences to the Calvo setup. Both models imply inflation and output stabilization goals. It is explained why the degree of distortion in the economy influences inflation aversion in the Rotemberg framework in a way that differs from the Calvo setup.

Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).