Ruin problems and myopic portfolio optimization in continuous trading

In continuous trading, ruin problems are important for several reasons. ln the first part of the paper a test criterion for bankruptcy is developed. In the present framework one implicitly assumes the investor's wealth to be different from zero, otherwise the model is not well-defined. It is of practical interest to be able to investigate if a certain stationary Markovian financial strategy may lead to ruin. If ruin can occur, its probability is found to satisfy a partial differential equation. In the second part of the paper, a portfolio optimization problem is investigated and solved using Doléans-Dade's exponential formula. The optimality criterion used is to maximize the expected rate of growth. Because of the special structure of the problem, we avoid the Bellman equation. This fact is fortunate, since the Bellman equation is often very complicated to solve analytically.