A relevant financial planning problem is the periodical rebalance of a portfolio of assets such that the portfolio’s total value exhibits certain characteristics. This problem can be modelled using a transition graph G to represent the future state space evolution of the corresponding economy and mathematically formulated as a linear programming problem. We present two different mathematical formulations of the problem. The first considers explicitly the set of the possible scenarios (scenario-based approach), while the second considers implicitly the whole set of scenarios provided by the graph G (graph-based approach). Unfortunately, for both the formulations the size of the corresponding linear programs can be huge even for simple financial problems. However, the graph-based approach seems to be a more powerful model, since it allows to consider a huge number of scenarios in a very compact formulation. The purpose of this paper is to present both heuristic and exact methods for the solution of large-scale multi-period financial planning problems using the graph-based model. In particular, in this paper we propose lower and upper bounds and three exact methods based on column, row and column/row generation, respectively. Since the methods based on column/row generation exploits simultaneously both the primal and the dual structure of the problem we call it Criss-Cross generation method. Computational results are given to prove the effectiveness of the proposed methods.

Exact methods for large-scale multi-period financial planning problems

BALDACCI, ROBERTO;BOSCHETTI, MARCO ANTONIO;
2009

Abstract

A relevant financial planning problem is the periodical rebalance of a portfolio of assets such that the portfolio’s total value exhibits certain characteristics. This problem can be modelled using a transition graph G to represent the future state space evolution of the corresponding economy and mathematically formulated as a linear programming problem. We present two different mathematical formulations of the problem. The first considers explicitly the set of the possible scenarios (scenario-based approach), while the second considers implicitly the whole set of scenarios provided by the graph G (graph-based approach). Unfortunately, for both the formulations the size of the corresponding linear programs can be huge even for simple financial problems. However, the graph-based approach seems to be a more powerful model, since it allows to consider a huge number of scenarios in a very compact formulation. The purpose of this paper is to present both heuristic and exact methods for the solution of large-scale multi-period financial planning problems using the graph-based model. In particular, in this paper we propose lower and upper bounds and three exact methods based on column, row and column/row generation, respectively. Since the methods based on column/row generation exploits simultaneously both the primal and the dual structure of the problem we call it Criss-Cross generation method. Computational results are given to prove the effectiveness of the proposed methods.
R. Baldacci; M. A. Boschetti; N. Christofides; S. Christofides
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/36702
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? ND
social impact