We consider the problem of L2-hedging of contingent claims in diffusion type models for securities markets. In contrast to a recent paper of Schweizer (1994) we insist on a non-negative wealth process corresponding to the optimal hedge portfolio. For this reason the usual projection methods...

The valuation of a Swing option for stocks under the additional constraint of a minimum time distance between two different exercise times is considered. We give an explicit characterization of its pricing function as the value function of a multiple optimal stopping problem. The solution of...

We present a general framework for considering investment in defaultable securities which — as special cases — includes both the firm value and the intensity based approach to credit risky bonds. In this framework, we construct a dynamically evolving portfolio of high-yield bonds where...

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....

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....

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...