Bankruptcy in long-term investments

Long-term portfolio management is an important issue in modern finance and practice. We have analysed various known continuous-time strategies in portfolio management, with a focus on bankruptcy probabilities under these strategies. We show that, for each strategy, there is a threshold in the target return rate. When the target return rate is set above this threshold, the application of the strategy for a long investment horizon leads to certain bankruptcy. For a target return rate lower than this threshold, bankruptcy never occurs. Bankruptcy probabilities under a finite investment horizon are also studied. An empirical study based on the Dow Jones Industrial Average Index confirms these results. By comparing the behaviour of these strategies in various parameter regions, we reveal connections among these seemingly different strategies.