The most common equity mandate in the financial industry is to try to outperform an externally given benchmark with known weights. The standard quantitative approach to do this is to optimize the portfolio over short time horizons consecutively, using one-period models. However, it is not clear...

There is no room in the classical Black-Scholes framework for the market view of an investor. The investor in derivatives needs to know the volatility of the underlying, that is the 'choppiness' of the market, but the direction is irrelevant. Suppose we have two stocks A and B having the same...

In contrast to their role in theory options are in practice not only traded for hedging purposes. Many investors also use them for speculation purposes. For these investors the Black-Scholes price serves only as an orientaTion, their decisions to buy, hold or hedge an option are also based on...

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 investigate a portfolio optimization problem under the threat of a market crash, where the interest rate of the bond is modeled as a Vasicek process, which is correlated with the stock price process. We adopt a non-probabilistic worst-case approach for the height and time of the market crash....

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...