The purpose of this paper is to investigate the possiblility to approximate computationally multistage stochastic linear programs with arbitrary underlying probability distributions by those with finite discrete probability distributions—to begin with, just for the special case of only the right-hand-side being random.

Forest harvest scheduling has been modeled using deterministic and stochastic programming models. Past models seldom address explicit spatial forest management concerns under the influence of natural disturbances. In this research study, we employ multistage full recourse stochastic programming models to explore the challenges and advantages of building spatial optimization models that account ...

In this note we focus attention on stochastic versions of the Ramsey growth model if either for a given time horizon expected value of the considered utility function should be maximized or if for infinite time horizon maximal average utility should be obtained. In contrast to the standard Ramsey economy growth model we assume that the production function considered in the economy model is infl...

In this paper, we present a generic Multistage Stochastic Programming (MSSP) model considering endogenous uncertainty in some of the parameters. To address the issue that the number of non-anticipativity (NA) constraints increases exponentially with the number of uncertain parameters and/or its realizations, we present a new theoretical property that significantly reduces the problem size and c...

This paper investigates some common interest rate models for scenario generation in financial applications of stochastic optimization. We discuss conditions for the underlying distributions of state variables which preserve convexity of value functions in a multistage stochastic program. Oneand multi-factor term structure models are estimated based on historical data for the Swiss Franc. An ana...

Stochastic programming with step decision rules, SPSDR, is an attempt to overcome the curse of computational complexity of multistage stochastic programming problems. SPSDR combines several techniques. The first idea is to work with independent experts. Each expert is confronted with a sample of scenarios drawn at random from the original stochastic process. The second idea is to have each expe...

We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal (minimum) value of the true problem. However, in order for such lower bound to be consistent one needs to employ the conditional sampling procedure. We also indicate that fi...

Multistage Stochastic Linear Programming (SLP) suffers from scenario explosion as the number of stages or the number of stochastic parameters increases. In this case, either one solves the SLP model approximately or one solves an approximation to the SLP model. In this situation it is useful to have some cost bound in order to assess the quality of approximated solutions. In this paper we intro...

We consider the case of multistage stochastic programming, in which decisions can adapt over time (i.e. at each stage) in response to observation of one or more random variables (uncertain parameters) and the time at which each observation occurs is decision-dependent. This is the difficult case of stochastic programming with endogeneous observation of uncertainty. Although such stochastic prog...

Forschungsplattform Alexandria https://www.alexandria.unisg.ch | 03.01.2016 We study bounding approximations for a multistage stochastic program with expected value constraints. Two simpler approximate stochastic programs, which provide upper and lower bounds on the original problem, are obtained by replacing the original stochastic data process by finitely supported approximate processes. We m...