Customer portfolio model driven by continuous-time Markov chains: An l<inf>2</inf> Lagrangian regularization method

Edgar Vazquez, Julio B. Clempner

Research output: Contribution to journalArticlepeer-review

Abstract

© 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 languageAmerican English
Pages (from-to)23-40
Number of pages18
JournalEconomic Computation and Economic Cybernetics Studies and Research
DOIs
StatePublished - 1 Jan 2020

Fingerprint Dive into the research topics of 'Customer portfolio model driven by continuous-time Markov chains: An l<inf>2</inf> Lagrangian regularization method'. Together they form a unique fingerprint.

Cite this