In the Black-Scholes-Merton model, as well as in more general stochastic models in finance, the price of an American option solves a parabolic variational inequality. When the variational inequality is discretized, one obtains a linear complementarity problem that must be solved at each time...

We propose a new computational method for the valuation of options in jump-diffusion models. The option value function for European and barrier options satisfies a partial integro-differential equation (PIDE). This PIDE is commonly integrated in time by implicit-explicit (IMEX) time...

This paper presents a novel method to price discretely-monitored single- and double-barrier options in Levy process-based models. The method involves a sequential evaluation of Hilbert transforms of the product of the Fourier transform of the value function at the previous barrier monitoring...

We present a fast and accurate method to compute exponential moments of the discretely observed maximum of a Levy process. The method involves a sequential evaluation of Hilbert transforms of expressions involving the characteristic function of the (Esscher transformed) Levy process. It can be...

This dissertation consists of two distinct lines of research e orts. Chapter 2 proposes a general methodology to seek robust solution to multi-stage stochastic optimization problems. Chapters 3, 4 and 5 all deal with models that arise from inventory management and dynamic pricing. Chapter 2...

In this thesis, we study the behavior of bankrupt stocks. Bankrupt stock is a special case of the Hard-to-Borrow stocks. Besides the general nice feature of the Hard-to-borrow feedback for the buy-in demand, the bankrupt stocks could exclude the diffusive effects. This nice property would modify...

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$...

This paper presents a set of schemes for the fast and accurate inversion of analytic characteristic functions. The schemes are based on sinc expansion approximation of functions that are analytic in a horizontal strip in the complex plane. A function in this class can be reconstructed highly...

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...

We consider option pricing problems in the stochastic volatility jump diffusion model with correlated and contemporaneous jumps in both the return and the variance processes (SVCJ). The option value function solves a partial integro-differential equation (PIDE). We discretize this PIDE in space...