Both barrier options and the Heston stochastic volatility model are omnipresent in real-life applications of financial mathematics. Therefore, we apply the Heath-Platen (HP) estimator as first introduced by Heath and Platen to price barrier options in the Heston model setting as an alternative...

In this paper we present some counter-examples to show that an uncritical application of the usual methods of continuous-time portfolio optimization can be misleading in the case of a stochastic opportunity set. Cases covered are problems with stochastic interest rates, stochastic volatility,...

In this article we include discrete dividends in the stock price model and solve a generalized portfolio optimization problem. For this, we develop a new discrete dividend model that allows for the possibility of early announcement and ensures that the drop of the stock price at the ex-dividend...

We present an expected utility maximisation framework for optimally controlling a portfolio of options. By combining the replication approach to option pricing with ideas of the martingale approach to (stock) portfolio optimisation we arrive at an explicit solution of the option portfolio...

We study numerical algorithms for reflected anticipated backward stochastic differential equations (RABSDEs) driven by a Brownian motion and a mutually independent martingale in a defaultable setting. The generator of a RABSDE includes the present and future values of the solution. We introduce...