Maximising Survival, Growth, and Goal Reaching Under Borrowing   Constraints
  In this paper, we consider three problems related to survival, growth, and goal reaching maximization of an investment portfolio with proportional net cash flow. We solve the problems in a market constrained due to borrowing prohibition. To solve the problems, we first construct an auxiliary market and then apply the dynamic programming approach. Via our solutions, an alternative approach is introduced in order to solve the problems defined under an auxiliary market. 
Haluk Yener
q-fin.PM