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).

Optimal progressive taxation in a model with endogenous skill supply.

This paper examines whether efficiency considerations require that optimal labour income taxation is progressive or regressive in a model with skill heterogeneity, endogenous skill acquisition and a production sector with capital-skill complementarity. We find that wage inequality driven by the resource requirements of skill-creation implies progressive labour income taxation in the steady-state as well as along the transition path from the exogenous to optimal policy steady-state. We find that these results are explained by a lower labour supply elasticity for skilled versus unskilled labour which results from the introduction of the skill acquisition technology.