Markets where asset prices follow processes with jumps are incomplete and any portfolio hedging against large movements in the price of the underlying asset must include other instruments. The standard approach in literature is to minimize the price variance of the hedging portfolio under a...

Guaranteed withdrawal benefits (GWBs) are long term contracts which provide investors with equity participation while guaranteeing them a secured income stream. Due to the long investment horizons involved, stochastic volatility and stochastic interest rates are important factors to include in...

Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of European and path-dependent options in a fast mean-reverting stochastic volatility setting. Our method is shown to be equivalent to those developed...

We develop a high frequency (HF) trading strategy where the HF trader uses her superior speed to process information and to post limit sell and buy orders. By introducing a multifactor mutually exciting process we allow for feedback effects in market buy and sell orders and the shape of the...