The paper investigates dynamic optimal portfolio strategies of utility maximizing portfolio managers in the presence of risk constraints. Especially we consider the risk, that the terminal wealth of the portfolio falls short of a certain benchmark level which is proportional to the stock price. This risk is measured by the Expected Utility Loss. We generalize the findings our previous papers to this case. Using the Black-Scholes model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results.

Thesis (doctoral)--Universität St. Gallen, 2003.

Univ., Diss.--Genève, 2007.

Univ., Diss.--St. Gallen, 2002.

St. Gallen, Univ., Diss., 2002.

Bachelor-Arbeit Univ. St. Gallen, 2006.

Master-Arbeit Univ. St. Gallen, 2006.

Techn. Universiẗat, Diss., 2005--Cottbus.

The presentation shows sample paths of stochastic processes in form of animations. Those stochastic procsses are usually used to model financial quantities like exchange rates, interest rates and stock prices. In the second part the solution of the Black-Scholes PDE using the finite difference method is illustrated. / Der Vortrag zeigt Animationen von Realisierungen stochstischer Prozesse, die zur Modellierung von Groessen im Finanzbereich haeufig verwendet werden (z.B. Wechselkurse, Zinskurse, Aktienkurse). Im zweiten Teil wird die Loesung der Black-Scholes Partiellen Differentialgleichung mittels Finitem Differenzenverfahren graphisch veranschaulicht.

In this paper, we study mathematical properties of a generalized bivariate Ornstein-Uhlenbeck model for financial assets. Originally introduced by Lo and Wang, this model possesses a stochastic drift term which influences the statistical properties of the asset in the real (observable) world. Furthermore, we generali- ze the model with respect to a time-dependent (but still non-random) volatility function. Although it is well-known, that drift terms - under weak regularity conditions - do not affect the behaviour of the asset in the risk-neutral world and consequently the Black-Scholes option pricing formula holds true, it makes sense to point out that these regularity conditions are fulfilled in the present model and that option pricing can be treated in analogy to the Black-Scholes case.