Por favor, use este identificador para citar o enlazar este ítem: http://repositoriodigital.ipn.mx/handle/123456789/21751
Título : Solving the mean–variance customer portfolio in Markov chains using iterated quadratic/Lagrange programming: A credit-card customer limits approach
Autor : Clepner Kerik, Julio Bernardo
Palabras clave : Mean–variance portfolio
Quadratic Lagrange programming
Credit-card portfolios
Credit-risk management
Customer-credit limits
Markov chains
Fecha de publicación : 9-mar-2015
Editorial : ELSEVIER
Resumen : In this paper we present a new mean–variance customer portfolio optimization algorithm for a class of ergodic finite controllable Markov chains. In order to have a realistic result we propose an iterated two-step method for solving the given portfolio constraint problem: (a) the first step is designed to optimize the nonlinear problem using a quadratic programming method for finding the long run fraction of the time that the system is in a given state (segment) and an action (promotion) is chosen and, (b) the second step is designed to find the optimal number of customers using a Lagrange programming approach. Both steps are based on the c-variable method to make the problem computationally tractable and obtain the optimal solution for the customer portfolio. The Tikhonov’s regularization method is used to ensure the convergence of the objective-function to a single optimal portfolio solution. We prove that the proposed method converges by the Weierstrass theorem: the objective function of the mean–variance customer portfolio problem decreases, it is monotonically non-decreasing and bounded from above. In addition, for solving the customer portfolio problem we consider both, a constant risk-aversion restriction and budget limitations. The constraints imposed by the system produce mixed strategies. Effectiveness of the proposed method is successfully demonstrated theoretically and by a simulated experiment related with credit-card and customer-credit limits approach for a bank.
URI : http://www.repositoriodigital.ipn.mx/handle/123456789/21751
ISSN : 0957-4174
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