We derive an expansion for the (expected) difference between the continuously monitored supremum and evenly monitored discrete maximum over a finite time horizon of a jump diffusion process with i.i.d. normal jump sizes. The monitoring error is of the form $a_0/N^{1/2}$ $ a_1/N^{3/2}$ $ \cdots$...

The simulation of a discrete sample path of a Levy process reduces to simulating from the distribution of a Levy increment. For a general Levy process with exponential moments, the inverse transform method proposed in Glasserman and Liu 2010 [24] is reliable and efficient. The values of the...

This paper presents a Hilbert transform method for pricing Bermudan options in Lévy process models. The corresponding optimal stopping problem can be solved using a backward induction, where a sequence of inverse Fourier and Hilbert transforms need to be evaluated. Using results from a sinc...

A new algorithm, which is based on the splitting-step idea and the penalization method, for reflected stochastic differential equation (RSDE) in the upper half-space R¹<sub >+</sub> is presented in this paper. After some important estimates about RSDEs and penalization ODEs are obtained, the local pathwise...