We consider the determination of portfolio processes yielding the highest worst-case bound for the expected utility from final wealth if the stock price may have uncertain (down) jumps. The optimal portfolios are derived as solutions of non-linear differential equations which itself are...

We present a new approach for continuous-time portfolio strategies that relies on the principle of value preservation. This principle was developed by Hellwig (1987) for general economic decision and pricing models. The key idea is that an investor should try to consume only so much of his...

We review some different approaches to treat the continuous-time portfolio problem under transaction costs and highlight the difficulties with their application to real-world tasks. In particular, we point out the problems and possibilities of using the Morton and Pliska (1995) approach and its...

We consider some relations between the minimal martingale measure and the value preserving martingale measure in a continuous-time securities market. Under the assumption of continuous share prices we show that under a structure condition both these martingale measures exist and indeed coincide....

We consider three applications of impulse control in financial mathematics, a cash management problem, optimal control of an exchange rate, and portfolio optimisation under transaction costs. We sketch the different ways of solving these problems with the help of quasi-variational inequalities....

In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will...

We study investment problems in a continuous-time setting and conclude that the proper control variables are elasticities to the traded assets or, in the case of stochastic interest rates, (factor) durations. This formulation of a portfolio problem allows us to solve the problems in a kind of...

In this paper a portfolio problem is considered where trading in the risky asset is stopped if a state process hits a predefined barrier. This state process need not to be perfectly correlated with the risky asset. We give a representation result for the value function and provide a verification...