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...

Lookback options have payoffs dependent on the maximum and/or minimum of the underlying price attained during the option’s lifetime. Based on the relationship between diffusion maximum and minimum and hitting times and the spectral decomposition of diffusion hitting times, this paper gives an...

This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount factor (SDF) is a positive semimartingale multiplicative...

We develop an eigenfunction expansion based value iteration algorithm to solve discrete time infinite horizon optimal stopping problems for a rich class of Markov processes that are important in applications. We provide convergence analysis for the value function and the exercise boundary, and...

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator....