Competitive analysis is concerned with minimizing a relativemeasure of performance. When applied to financial trading strategies,competitive analysis leads to the development of strategies with minimumrelative performance risk. This approach is too inflexible. Manyinvestors are interested in managing their risk: they may be willing toincrease their risk for some form of reward. They may also have someforecast of the future. We extend competitive analysis to provide aframework in which investors can develop optimal trading strategiesbased on their risk tolerance and forecast. We first define notions ofrisk and reward that are smooth extensions of classical competitiveanalysis. We then illustrate our ideas using the ski-rental problem.Finally, we analyze a financial game, the unidirectional conversionproblem. In particular, we present an optimal risk-tolerant algorithmfor the forecast that prices will reach a certain level at some pointduring the game, and give numerical results of the investor's reward formaking such a forecast
展开▼
