The technique described in this paper has implications for risk management for institutions, banks, government entities, pension plans, and insurance companies. The paper describes a generic financial planning problem as a multistage stochastic program, modeled using a network graph that provides a visual reference for the financial planning system. A large number of scenarios can be investigated in order to cover different aspects of uncertainty, and to provide a reasonable representation of the universe being modeled. Assets and liabilities are integrated in order to address the whole financial planning problem and to comply with accounting practices.

The multistage financial planning model is described in the first section, including details about objective functions, the multiperiod framework, the modeling of stochastic parameters, and the integration of assets and liabilities.

Section 2 describes a computational experiment. Due to the large size of the problem, the experiment is realized on high-performance computers, including parallel and distributed machines. Solution algorithms (parallel direct solvers and decomposition algorithms) are presented for different numbers of scenarios (64, 512, 2,048, and 4,096), and for different number of processors (16, 32, 64, and 128).

In section 3, the authors consider dynamic stochastic control models and detail a global algorithm. They discuss the difficulties of developing a stochastic control framework. Conclusions and potential future development directions close this valuable paper. The references are adequate, and illustrate the state of the art in the multistage optimization field.