In this chapter we study the problem of valuing a (possibly defaultable) derivative asset
contingent on the underlying economic state modeled as a Markov process. To gain …

Parameter estimation in stochastic differential equations and stochastic partial differential
equations is the science, art and technology of modelling complex phenomena and making …

The Pearson diffusions form a flexible class of diffusions defined by having linear drift and
quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical …

We are interested in strong approximations of one-dimensional SDEs which have non-
Lipschitz coefficients and which take values in a domain. Under a set of general …

This paper develops a spectral expansion approach to the valuation of contingent claims
when the underlying state variable follows a one-dimensional diffusion with the infinitesimal …

Flexible stationary diffusion-type models are developed that can fit both the marginal
distribution and the correlation structure found in many time series from, for example, finance …

This paper provides the mathematical foundation for polynomial diffusions. They play an
important role in a growing range of applications in finance, including financial market …

Let X be a multidimensional diffusion with jumps. We provide sets of conditions under which:
X fulfils the ergodic theorem for any initial distribution; and X is exponentially β-mixing …

In this book, we study stochastic volatility models and methods of pricing, hedging, and
estimation. Among models, we will study models with heavy tails and long memory or long …

Motivated by the industry practice of pairs trading, we study the optimal timing strategies for
trading a mean-reverting price spread. An optimal double stopping problem is formulated to …