We introduce the optimal-drift model for the approximation of a lognormal stock price process by an accelerated binomial scheme. This model converges with order o(1/N), which is superior compared to today’s benchmark methods. Our approach is based on the observation that risk-neutral binomial...

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 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....

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...

In a general semi-martingale financial market with possibly nonlinear wealth dynamics, incomplete information, and ambiguity, we show that the optimal consumption decision of an agent with logarithmic preferences can be separated from the agent's investment decisions. Using minimal assumptions...

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....