Catálogo de publicaciones - libros

The aim of this paper is to provide an overview of existing concepts of robustness and to identify promising directions for coping with uncertainty and risks surrounding on-going global changes. Unlike statistical robustness, general decision problems may have rather different facets of robustness. In particular, a key issue is the sensitivity of decisions with respect to low-probability catastrophic events. That is, robust decisions in the presence of catastrophic events are fundamentally different from decisions ignoring them. Specifically, proper treatment of extreme catastrophic events requires new sets of feasible decisions, adjusted to risk performance indicators, and new spatial, social and temporal dimensions. The discussion is deliberately kept at a level comprehensible to a broad audience through the use of simple examples that can be extended to rather general models. In fact, these examples often illustrate fragments of models that are being developed at IIASA.

When working with stochastic financial models, one exploits various simplifying assumptions concerning the model, its stochastic specification, parameter values, etc. In addition, approximations are used to get a solution in an efficient way. The obtained results, recommendations for the risk and portfolio manager, should be then carefully analyzed. This is done partly under the heading “stress testing”, which is a term used in financial practice without any generally accepted definition. In this paper we suggest to exploit the contamination technique to give the “stress test” a more precise meaning. Using examples from portfolio and risk management we shall point out the directly applicable cases and will discuss also limitations of the proposed method.

Uncertainty is a key issue in many public debates and policy making, including climate change, pension systems, and integrated management of catastrophic risks. Rational treatment of uncertainty in many such situations requires new methods not only for the appropriate handling of endogenous uncertainties but also for modeling complex problems.

The paper first outlines the key issues related to uncertainties and risks, including some pitfalls of using traditional methods in situations when they are inappropriate. Then, new methods of modeling endogenous uncertainties and catastrophic risks are summarized. Next, structured modeling technology developed for handling the whole modeling process of model-based support for solving complex problems is discussed.

The development of the presented methods has been motivated by actual policymaking issues, and the methods have been applied to complex problems. However, the presentation is deliberately kept at a level comprehensible to a broad audience.

This chapter is concerned with the estimation of the reliability of structures in view of physical uncertainties encountered due to the inherent variability in structural properties and loads. In this respect, methods based on the traditional Monte Carlo simulation method are employed to deal with probabilistically modeled uncertainties. Hence, suitable variance reduction techniques and efficient computational procedures are presented, in order to alleviate the high processing demands associated with Monte Carlo computations and make the overall reliability estimation process more tractable in practice. The focus of this chapter is on statistically high-dimensional problems, which involve large numbers of random variables. The merits of some of the techniques and algorithms described are demonstrated with two application examples.

Problems from plastic limit load or shakedown analysis and optimal plastic design are based on the convex yield criterion and the linear equilibrium equation for the generic stress (state) vector . The state or performance function *() is defined by the minimum value function of a convex or linear program based on the basic safety conditions of plasticity theory: A safe (stress) state exists then if and only if * < 0, and a safe stress state cannot be guaranteed if and only if * ≥ 0. Hence, the probability of survival can be represented by = (*((), ) < 0).

Using FORM, the probability of survival is approximated then by the well-known formula ∼ (||*||) where ||*|| denotes the length of a so-called -point, hence, a projection of the origin 0 to the failure domain (transformed to the space of normal distributed model parameters () = (())). Moreover, = ()denotes the distribution function of the standard N(0,1) normal distribution. Thus, the basic reliability condition, used e.g. in reliability-based optimal plastic design or in limit load analysis problems, reads ||*|| ≥ () with a prescribed minimum probability . While in general the computation of the projection * is very difficult, in the present case of elastoplastic structures, by means of the state function * = *() this can be done very efficiently: Using the available necessary and sufficient optimality conditions for the convex or linear optimization problem representing the state function * = *(), an parameter optimization problem can be derived for the computation of a design point *. Simplifications are obtained in the standard case of piecewise linearization of the yield surfaces.

In addition, several different response surface methods including the standard response surface method are also applied to compute a -point * in order to reduce the computational time as well as having more accurate results than the first order approximation methods by using the obtained response surface function with any simulation methods such as Monte Carlo Simulation. However, for the problems having a polygon type limit state function, the standard response surface methods can not approximate well enough. Thus, a response surface method based on the piecewise regression has been developed for such problems. Applications of the methods developed to several types of structures are presented for the examples given in this paper.

We make a first attempt to give an extreme value analysis of data, connected to catastrophic events. While the data are readily accessible from SWISSRE, their analysis doesn’t seem to have been taken up. A first set refers to insured claims over the last 35 years; the second deals with victims from natural catastrophes. Together these sets should provide ample proof that extreme value analysis might be able to catch some essential information that traditional statistical analysis might overlook. We finish with a number of cautious remarks.

We present an approach to probabilistic modelling of static and dynamic scenes for the purpose of scene interpretation and -prediction. Our system, utilizing Bayesian Network Fragments as relational extension to Bayesian networks, provides modelling in an object-oriented way, handling modular repetitivities and hierarchies within domains. We specify a knowledge-based framework, which maintains both partonomy- and taxonomy-hierarchies of entities, and describe an interpretation method exploiting these. The approach offers arbitrary reasoning facilities, where low level perceptive information as well as abstract context knowledge within scenes can be either given as evidence or queried.

The treatment of spatial characteristics through probability distributions makes it possible to use stochastic optimization methods and to obtain efficiency results and competitive equilibrium prices for general equilibrium models with discrete choices in spatial continuum. Along these lines, and combining results from stochastic optimization with principles established by Aumann and Hildenbrand for economies with continuum of traders the paper develops a practical modeling framework that can combine the spatially distributed aspects of land-use with processes such as market clearing or telecommunication investments concentrated at specific points. It also presents associated stochastic algorithms for numerical implementation. We discuss both a general equilibrium version in which all consumers meet their own budget, and a welfare maximizing version with transfers adjusting among consumer groups for which we formulate a dual approach that solely depends on a finite number of prices.

Global change processes raise new estimation problems challenging the conventional statistical methods. These methods are based on the ability to obtain observations from unknown true probability distributions, whereas the new problems require recovering information from only partially observable or even unobservable variables. For instance, aggregate data exist at global and national level regarding agricultural production, occurrence of natural disasters, on incomes, etc. without providing any clue as to possibly alarming diversity of conditions at local level. “Downscaling” methods in this case should achieve plausible estimation of local implications emerging from global tendencies by using all available evidences.

The aim of this paper is to develop a sequential downscaling method, which can be used in a variety of practical situations. Our main motivation for this was the estimation of spatially distributed crop production, i.e., on a regular grid, consistent with known national-level statistics and in accordance with geographical datasets and agronomic knowledge. We prove convergence of the method to a generalized cross-entropy maximizing solution. We also show that for specific cases this method is reduced to known procedures for estimating transportation flows and doubly stochastic matrices.

Linear dynamical control systems subject to uncertain but bounded disturbances are considered. The bounds imposed on the disturbances depend on the control magnitude and grow with the control. This situation is typical for the cases where the disturbance is due to the inaccuracy of the control implementation and often takes place in engineering applications such as transportation, aerospace, and robotic systems.

Under certain assumptions, the minimax control problem is formulated and solved. The explicit expressions for the optimal control (both open-loop and feedback) are obtained that provide the minimax to the given performance index for arbitrary but bounded disturbances. Examples are given.