Institute of Electrical and Electronics Engineers. Transactions on Automatic Control (IEEE Trans. Automat. Control) (20040101), 49, no.~3, 447-457. ISSN: 0018-9286 (print).eISSN: 1558-2523.
In this paper a dynamic portfolio optimization problem in discrete time is considered. The classical Markowitz problem of mean-variance optimization is generalized by including bounds for the probability of bankruptcy in each period. Using Chebyshev's inequality, these probability bounds are included in the optimization problem as additional mean-variance bounds for the state variables. This makes the problem nonseparable in time and thus unfeasible for the classical dynamic programming approach. Therefore a primal-dual method is used to find the optimal solution.