Can continuous-time portfolio optimization really be applied?

Solving the continuous-time portfolio problem is one of the major research areas in financial management mathematics. While there have been many innovations and theoretical breakthroughs in this area, it has been no success in terms of practical applications in banks and on stock exchanges. The main reason for this is that the presence of transaction costs leads to immediate ruin by following the theoretically optimal trading strategies. In our contribution we introduce the continuous-time portfolio problem, survey some important innovations and suggest two practical ways to deal with the transaction cost problem, but still benefit from results derived in the continuous-time setting. One of our suggestions is based on the concept of the relaxed investor, while the other one benefits from a reinterpretation of a portfolio problem with an unrealistic cost structure.