© 2020, Bucharest University of Economic Studies. All rights reserved. This paper provides a solution to the customer portfolio for a given fixed desired expected rate of return under constraints based. We restrict the solution to a class of finite, ergodic, controllable continuous-time, finite-state Markov chains. We propose a regularized Lagrange method for the portfolio representation that ensures the strong convexity of the objective function and the existence of a unique solution of the portfolio. The solution is obtained by using the standard Lagrange method introducing the positive parameters θ and δ, and the Lagrange vector-multipliers μ0 and μ1 for the equality and inequality constraints, respectively, and forming the Lagrangian. We prove that if the ratioδθn tends to zero, then the solution of the original portfolio converges to a unique solution withn the minimal weighted norm. We introduce a recurrent procedure based on the projection-gradient method for finding the extremal points of the portfolio. In addition, we prove the convergence of the method. A numerical example validates the effectiveness of the regularized portfolio Lagrange method.
|Original language||American English|
|Number of pages||18|
|Journal||Economic Computation and Economic Cybernetics Studies and Research|
|State||Published - 1 Jan 2020|