We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the al...

We define a risk-averse nonanticipative feasible policy for multistage stochastic programs and propose a methodology to implement it. The approach is based on dynamic programming equations written for a risk-averse formulation of the problem. This formulation relies on a new class of multiperiod risk functionals called extended polyhedral risk measures. Dual representations of such risk functio...

the hub location decision is a long term investment and any changes in it take considerable time and money. in real situations, some parameters are uncertain hence, deterministic models cannot be more efficient. the ability of two-stage stochastic programming is to make a long-term decision by considering effects of it in short term decisions simultaneously. in the two-stage stochastic programm...

We consider an asset-liability management (ALM) problem for a defined benefit pension fund (PF). The PF manager is assumed to follow a maximal fund valuation problem facing an extended set of risk factors:  due to the longevity of the    PF members, the inflation affecting salaries in real terms and future incomes, interest rates and market factors affecting jointly the PF liability and asset p...

Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely challenging problems. A common formulation for these problems is a dynamic programming formulation involving nested cost-to-go functions. In the linear setting, the cost-to-go functions are convex polyhedral, and decomposition algorithms, suc...

Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely challenging problems. A common formulation for these problems is a dynamic programming formulation involving nested cost-to-go functions. In the linear setting, the cost-to-go functions are convex polyhedral, and decomposition algorithms, suc...

We consider a class of multistage stochastic linear programs in which at each stage a coherent risk measure of future costs is to be minimized. A general computational approach based on dynamic programming is derived that can be shown to converge to an optimal policy. By computing an inner approximation to future cost functions, we can evaluate an upper bound on the cost of an optimal policy, a...

The solution of a multistage stochastic programming problem needs a suitable representation of uncertainty which may be obtained through a satisfactory scenario tree construction. Unfortunately there is a trade-off between the level of accuracy in the description of the stochastic component and the computational tractability of the resulting scenario-based problem. In this contribution we addre...

This chapter proposes a multistage stochastic optimization framework that dynamically updates the purchasing and distribution decisions of emergency commodities in the aftermath of an earthquake. Furthermore, the models consider the risk of exceeding the budget levels at any stage through chance constraints, which are then converted to Conditional Value-at-Risk constraints. Compared to the prev...

Every multistage stochastic programming problem with recourse (MSPR) contains a filtration process. In this research, we created a notation that makes the filtration process the central syntactic construction of the MSPR. As a result, we achieve lower redundancy and higher modularity than is possible with the mathematical notation commonly associated with stochastic programming. StAMPL is a mod...