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...

In this paper, we first propose a portfolio management model where the objective is to balance equity and liability. The asset price dynamics includes both permanent and temporary price impact, where the permanent impact is a linear function of the cumulative trading amount and the temporary...

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 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...

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...