In financial and actuarial modeling and other areas of application, stochastic differential
equations with jumps have been employed to describe the dynamics of various state …

During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

Since the introduction of ARCH models close to 40 years ago, a wide range of models for
volatility estimation and prediction have been developed and integrated into asset …

This paper presents a review of time series filtering and its applications in mathematical
finance. A summary of results of recent empirical studies with market data are presented for …

A financial market with one bond and one stock is considered where the risk free interest
rate, the appreciation rate of the stock and the volatility of the stock depend on an external …

We discuss jump-diffusion type models for financial market as well as methods for pricing
and hedging of contingent claims in such markets. We consider both, asset price and term …

The main goal of filtering is to obtain, recursively in time, good estimates of the state of a
stochastic dynamical system based on noisy partial observations of the same. In settings …

The theory of nonlinear filtering concerns the optimal estimation of a Markov signal in noisy
observations. Such estimates necessarily depend on the model that is chosen for the signal …

We deal with the filtering problem of a general jump diffusion process, X, when the
observation process, Y, is a correlated jump diffusion process having common jump times …

This paper is concerned with nonlinear filtering of the coefficients in asset price models with
stochastic volatility. More specifically, we assume that the asset price process S=(S t) t≥ 0 is …