Maximizing survival,growth and goal reaching under borrowing constraints

In this paper, we consider the survival, growth and goal reaching maximization problems treated in Browne Math. Oper. Res., 1997, 22, 468–493] and solve them in a market constrained due to borrowing prohibition. To solve the problems, we first construct an auxiliary market introduced by Cvitanic and Karatzas Ann. Appl. Probab., 1992, 2, 767–818] 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.