This paper proposes a unified framework for portfolio optimization, derivative pricing, modeling and risk measurement in financial markets with security price processes that exhibit intensity based jumps. It is based on the natural assumption that investors prefer more for less, in the sense...

The growth optimal portfolio (GOP) plays an important role in finance, where it serves as the numeraire portfolio, with respect to which contingent claims can be priced under the real world probability measure. This paper models the GOP using a time dependent constant elasticity of variance...

We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization...

We investigate the existence of affine realizations for interest rate term structure models driven by Levy processes. Using as numeraire the growth optimal portfolio, we model the interest rate term structure under the real-world probability measure, and hence, we do not need the existence of an...

Market models which re ect stylised properties of the interest rate term structure are widely used for modelling and pricing interest rate derivatives. We consider a market model involving the short rate and a diversied global stock index. We illustrate the stylised properties of the interest...

Short rates of interest are considered within in the term structure model of Eberlein-Raible [6] driven by a Lévy process. It is shown that they are Markovian if and only if the volatility function factorizes. This extends results of Caverhill [5] for the Wiener process and of Eberlein, Raible...

The geometric Brownian motion is the solution of a linear stochastic differential equation in the Itô-sense. If one adds to the drift term a possible nonlinear time delayed term and starts with a nonnegative initial process then the process generated in this way, may hit zero and may oscillate...

Assume L is a non-deterministic real valued Lévy process and f is a smooth function on [0,t]