An Algorithmic Approach to Non-self-financing Hedging in a Discrete-Time   Incomplete Market
  We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two stage process that first determines admissible model parameters that correspond to the market price of the option being hedged. The second stage applies various merit functions to bootstrapped samples of model residuals to choose an optimal set of model parameters from the admissible set. Results are presented for options traded on the New York Stock Exchange. 
N. Josephy, L. Kimball, A. Nagaev, M. Pasniewski, V. Steblovskaya