Groupe d’études et de recherche en analyse des décisions

G-98-12

Some Optimization Models in Risk Management I

Since the beginning of 90's, risk management has become an important topic of research for both the academic and financial institutions. Progress in globalization of financial markets, extensive development of complex investment instruments and fluctuation of interest rates have led to the high volatility of the financial markets. It is crucial for the investment consultants to manage those resulting risks by dynamically balancing the firm's assets and liabilities to achieve its objectives. Some multi-period models were considered in the early 90's by S.A. Zenios, H. Dahl and others. However, those models lead to some large scale complex nonlinear problems. A multi-stage stochastic optimization model was developed by John M. Murvey et al. in 1995 and solved successfully on a high power main frames. Most recently, a dynamically balanced long-term financial planning model was formulated with large reduction of random variables by C. D. Maranas et al. (1997) and the resulting nonconvex optimization problem was solved by Bender's Decomposition Method.

We have found that a medium size version of the former problem can be decomposed into a number of nonlinear sub-problems, while the latter can be further elaborated to respond more accurately to the recent turbulent financial market. Both of these models can be solved by some of the efficient heuristic algorithms we developed for solving nonlinear and mixed integer nonlinear problems in a work-station on powerful personal computer.

, 12 pages

Ce cahier a été révisé en juin 1998