Integrated chance constraints: reduced forms and an algorithm

We consider integrated chance constraints (ICC), which provide quantitative alternatives for traditional chance constraints.We derive explicit polyhedral descriptions for the convex feasible sets induced by ICCs, for the case that the underlying distribution is discrete. Based on these reduced forms, we propose an efficient algorithm for this problem class. The relation to conditional value-at-risk models and (simple) recourse models is discussed, leading to a special purpose algorithm for simple recourse models with discretely distributed technology matrix. For both algorithms, numerical results are presented.

ALM model for pension funds : numerical results for a prototype model

A multistage mixed-integer stochastic programming model is formulated for an Asset Liability Management problem for pension funds. Since these models are too difficult to solve for realistically sized problems, a heuristic is described. Numerical results for several instances of a prototype model are presented and discussed.

Total variation bounds on the expectation of periodic functions with applications to recourse approximations

We derive a lower and upper bound for the expectation of periodic functions, depending on the total variation of the probability density function of the underlying random variable. Using worst-case analysis we derive tighter bounds for functions that are periodically monotone. These bounds can be used to evaluate the performance of approximations for both continuous and integer recourse models. In this paper, we introduce a new convex approximation for totally unimodular recourse models, and we show that this convex approximation has the best worst-case error bound possible, improving previous bounds with a factor 2. Moreover, we use similar analysis to derive error bounds for two types of discrete approximations of continuous recourse models with continuous random variables. Furthermore, we derive a tractable Lipschitz constant for pure integer recourse models

An ALM model for pension funds using integrated chance constraints

We discuss integrated chance constraints in their role of short-term risk constraints in a strategic ALM model for Dutch pension funds. The problem is set up as a multistage recourse model, with special attention for modeling short-term risk prompted by the development of new guidelines by the regulating authority for Dutch pension funds. The paper concludes with a numerical illustration of the importance of such short-term risk constraints