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Georg Pflug

University of Vienna, Department of statistics and Operations Research, Faculty Member

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Born in 1951, Georg Pflug studied Law, Mathematics and Statistics at the University of Vienna. He was Professor at the University of Giessen, Germany and is now Full Professor at the University of Vienna and Head of the Computational Risk Management Group. He is also part time research scholar at the International Institute of Applied Systems Analysis, Laxenburg, Austria. Georg Pflug's interests include Stochastic Modeling, Stochastic Optimization, Measuring and Managing of Risks and Applications in Finance, Insurance and Energy, Pension Funds and Insurance. He is author of 4 books, editor of 6 books, and more than 100 publications in refereed journals.

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Papers by Georg Pflug

Understanding the role of climate change in disaster mortality: Empirical evidence from Nepal

Climatic disaster impacts, such as loss of human life as its most severe consequence, have been r... more Climatic disaster impacts, such as loss of human life as its most severe consequence, have been rising globally. Several studies argue that the growth in exposure, such as population, is responsible for the rise and the role of climate change is not evident. While disaster mortality is highest in low-income countries, existing studies focus mostly on developed countries. Here we address this impact attribution question in the context of the Global South using disaster-specific mixed-effects regression models. We show that the rise in landslide and flood mortality in a low-income country Nepal between 1992-2021 is attributable primarily to the increased precipitation extremes. An increase in one standardized unit in maximum one-day precipitation increases flood mortality by 33%, and heavy rain days increase landslide mortality by 45%. A one-unit increase in per capita income decreases landslide and flood mortality by 30% and 45%, respectively. Population density does not show signifi...

Understanding the role of climate change in disaster mortality: Empirical evidence from the Global South

Climatic disaster impacts, such as loss of human life as its most severe consequence, have been r... more Climatic disaster impacts, such as loss of human life as its most severe consequence, have been rising globally. Several studies argue that population growth is responsible for the rise, and the role of climate change is not evident. While disaster mortality is highest in low-income countries, existing studies focus mostly on developed countries. Here we address this impact attribution question in the context of the Global South using disaster-specific mixed-effects regression models. We show that the rise in landslide and flood mortality in a low-income country such as Nepal between 1992-2021 is primarily attributable to increased precipitation extremes. An increase in one standardized unit in maximum one-day precipitation increases flood mortality by 33%, and heavy rain days increase landslide mortality by 45%. Similarly, a one-unit increase in per capita income decreases landslide and flood mortality by 30% and 45%, respectively. Population density does not show significant effects.

ScenTrees.jl: A Julia Package for Generating Scenario Trees and Scenario Lattices for Multistage Stochastic Programming

Journal of Open Source Software, 2020

Stochastic processes have random and uncertain outcomes. Decisions for stochastic problems involv... more Stochastic processes have random and uncertain outcomes. Decisions for stochastic problems involving such processes must be made at the different stages of the problem. Mathematical problems with such uncertain parameters, described by an underlying probability distribution, are sometimes intractable to solve. For algorithmic treatment, such programs should be approximated by simpler ones, in the same manner as functions are represented as vectors on finite grids on digital computers. In most applications, these underlying distributions are approximated by discrete distributions with a finite number of scenarios, or possible realizations, for the random variables. This approximation procedure is often called scenario generation.

On Dynamic Decomposition of Multistage Stochastic Programs

It is well known that multistage programs, which maximize expectation or expected utility, allow ... more It is well known that multistage programs, which maximize expectation or expected utility, allow a dynamic programming formulation, and that other objectives destroy the dynamic programming character of the problem. This paper considers a risk measure at the final stage of a multistage stochastic program. Although these problems are not time consistent, it is shown that optimal decisions evolve as a martingale. A verification theorem is provided, which characterizes optimal decisions by enveloping sub-and supermartingales. To obtain these characterizations the idea of a constant risk profile has to be given up and instead a risk profile, which varies over time, has to be accepted. The basis of the analysis is a new decomposition theorem for risk measures, which is able to recover the genuine risk measure by measuring risk conditionally.

Climate change and climate insurance. The case of Malawi

IOP Conference Series: Earth and Environmental Science, 2009

This article was submitted without an abstract, please refer to the full-text PDF file.

Time-inconsistent multistage stochastic programs: Martingale bounds

European Journal of Operational Research, 2016

It is well known that multistage programs, which maximize expectation or expected utility, allow ... more It is well known that multistage programs, which maximize expectation or expected utility, allow a dynamic programming formulation, and that other objectives destroy the dynamic programming character of the problem. This paper considers a risk measure at the final stage of a multistage stochastic program. Although these problems are not time consistent, it is shown that optimal decisions evolve as a martingale. A verification theorem is provided, which characterizes optimal decisions by enveloping sub-and supermartingales. To obtain these characterizations the idea of a constant risk profile has to be given up and instead a risk profile, which varies over time, has to be accepted. The basis of the analysis is a new decomposition theorem for risk measures, which is able to recover the genuine risk measure by measuring risk conditionally.

Disaster Risk Transfer for Developing Countries

Financing disaster recovery often diverts resources from development, which can have long-term ef... more Financing disaster recovery often diverts resources from development, which can have long-term effects on economic growth and the poor in developing countries. Moreover, post-disaster assistance, while important for humanitarian reasons, has failed to meet the needs of developing countries in reducing their exposure to disaster risks and assuring sufficient funds to governments and individuals for financing the recovery process. The

Modeling financial disaster risk management in developing countries

The public sector plays a major role in reducing the long-term economic repercussions of disaster... more The public sector plays a major role in reducing the long-term economic repercussions of disasters by repairing damaged infrastructure and providing financial assistance to households and businesses. If critical infrastructure is not repaired in a timely manner, there can be serious effects on the economy and the livelihoods of the population. The repair of public infrastructure, however, can be a

Approximations for Probability Distributions and Stochastic Optimization Problems

International Series in Operations Research & Management Science, 2011

In this chapter, an overview of the scenario generation problem is given. After an introduction, ... more In this chapter, an overview of the scenario generation problem is given. After an introduction, the basic problem of measuring the distance between two single-period probability models is described in Section 15.2. Section 15.3 deals with finding good single-period scenarios based on the results of the first section. The distance concepts are extended to the multi-period situation in Section 15.4. Finally, Section 15.5 deals with the construction and reduction of scenario trees.

A Distance For Multistage Stochastic Optimization Models

SIAM Journal on Optimization, 2012

We describe multistage stochastic programs in a purely in-distribution setting, i.e. without any ... more We describe multistage stochastic programs in a purely in-distribution setting, i.e. without any reference to a concrete probability space. The concept is based on the notion of nested distributions, which encompass in one mathematical object the scenario values as well as the information structure under which decisions have to be made. The nested distance between these distributions is introduced, which turns out to be a generalization of the Wasserstein distance for stochastic two-stage problems. We give characterizations of this distance and show its usefulness in examples. The main result states that the difference of the optimal values of two multistage stochastic programs, which are Lipschitz and differ only in the nested distribution of the stochastic parameters, can be bounded by the nested distance of these distributions. This theorem generalizes the well-known Kantorovich-Rubinstein Theorem, which is applicable only in two-stage situations, to multistage. Moreover, a dual characterization for the nested distance is established. The setup is applicable both for general stochastic processes and for finite scenario trees. In particular, the nested distance between general processes and scenario trees is well defined and becomes the important tool for judging the quality of the scenario tree generation. Minimizing-at least heuristically-this distance is what good scenario tree generation is all about.

Refocusing Disaster Aid

Science, 2005

With new modeling techniques for estimating and pricing the risks of natural disasters, the donor... more With new modeling techniques for estimating and pricing the risks of natural disasters, the donor community is now in a position to help the poor cope with the economic repercussions of disasters by assisting before they happen. Such assistance is possible with the advent of novel insurance instruments for transferring catastrophe risks to the global financial markets. Donor-supported risk-transfer programs not only would leverage limited disaster-aid budgets but also would free recipient countries from depending on the vagaries of postdisaster assistance. Both donors and recipients stand to gain, especially because the instruments can be closely coupled with preventive measures.

Stochastic Dynamic Programming Using Optimal Quantizers

The 1/N investment strategy is optimal under high model ambiguity

Journal of Banking & Finance, 2012

The 1/N investment strategy, i.e. the strategy to split one's wealth uniformly between the availa... more The 1/N investment strategy, i.e. the strategy to split one's wealth uniformly between the available investment possibilities, recently received plenty of attention in the literature. In this paper, we demonstrate that the uniform investment strategy is rational in situations where an agent is faced with a sufficiently high degree of model uncertainty in the form of ambiguous loss distributions. More specifically, we use a classical risk minimization framework to show that, for a broad class of risk measures, as the uncertainty concerning the probabilistic model increases, the optimal decisions tend to the uniform investment strategy. To illustrate the theoretical results of the paper, we investigate the Markowitz portfolio selection model as well as Conditional Value-at-Risk minimization with ambiguous loss distributions. Subsequently, we set up a numerical study using real market data to demonstrate the convergence of optimal portfolio decisions to the uniform investment strategy.

On the Glivenko-Cantelli problem in stochastic programming: Mixed-integer linear recourse

Mathematical Methods of Operations Research, 1998

Expected recourse functions in linear two-stage stochastic programs with mixed-integer second sta... more Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original expected recourse function is established.

Configurations of series-parallel networks with maximum reliability

Microelectronics Reliability, 1996

The optimal design problem for networks with 3-state components is the following: select from a g... more The optimal design problem for networks with 3-state components is the following: select from a given class of networks with n components, each of which can be operative or experience an open-mode or a shorted-mode failure state, the network with maximum reliability. We present an algorithm for solving this problem in the case of %stage seriesparallel networks, i. e., networks consisting of a number of series configurations linked in parallel or vice versa. For practically relevant network sizes (up to 100 components), the algorithm is fast.

Modelling the Indirect and Fiscal Risks from Natural Disasters Using the CatSim Model

by Reinhard Mechler, Keith Williges, Anna Timonina-Farkas, and Georg Pflug

On Distributionally Robust Multiperiod Stochastic Optimization (joint with G. Pflug)

by Georg Pflug and Bita Analui

The paper considers model uncertainty for multistage stochastic programs. The data and informatio... more The paper considers model uncertainty for multistage stochastic programs. The data and information structure of the baseline model is a tree, on which the decision problem is defined. We consider "ambiguity neighborhoods" around this tree as alternative models which are close to the baseline model. Closeness is defined in terms of a distance for probability trees, called the nested distance. This distance is appropriate for scenario models of multistage stochastic optimization problems as was demonstrated in (Pflug and Pichler, 2012). The ambiguity model is formulated as a minimax problem, where the the optimal decision is to be found, which minimizes the maximal objective function, within the ambiguity set. We give a setup for studying saddle point properties of the minimax problem. Moreover, we present solution algorithms for finding the minimax decisions at least asymptotically. As an example, we consider a multiperiod stochastic production/inventory control problem with weekly ordering. The stochastic scenario process is given by the random demands for two products. We find the worst trees within the ambiguity set and determine a solution which is robust w.r.t. model uncertainty. It turns out that the probability weights of the worst case trees are concentrated on few very bad scenarios.

Pricing of Energy Contracts: From Replication Pricing to Swing Options

by Georg Pflug and Raimund Kovacevic

International Series in Operations Research & Management Science, 2013

Measuring Systemic Risk: Structural Approaches

by Georg Pflug and Raimund Kovacevic

Theory and Practice, 2015

Properties And Computation Of Value At Risk Efficient Portfolios Based On Historical Data

SSRN Electronic Journal, 2000

Understanding the role of climate change in disaster mortality: Empirical evidence from Nepal

Climatic disaster impacts, such as loss of human life as its most severe consequence, have been r... more Climatic disaster impacts, such as loss of human life as its most severe consequence, have been rising globally. Several studies argue that the growth in exposure, such as population, is responsible for the rise and the role of climate change is not evident. While disaster mortality is highest in low-income countries, existing studies focus mostly on developed countries. Here we address this impact attribution question in the context of the Global South using disaster-specific mixed-effects regression models. We show that the rise in landslide and flood mortality in a low-income country Nepal between 1992-2021 is attributable primarily to the increased precipitation extremes. An increase in one standardized unit in maximum one-day precipitation increases flood mortality by 33%, and heavy rain days increase landslide mortality by 45%. A one-unit increase in per capita income decreases landslide and flood mortality by 30% and 45%, respectively. Population density does not show signifi...

Understanding the role of climate change in disaster mortality: Empirical evidence from the Global South

Climatic disaster impacts, such as loss of human life as its most severe consequence, have been r... more Climatic disaster impacts, such as loss of human life as its most severe consequence, have been rising globally. Several studies argue that population growth is responsible for the rise, and the role of climate change is not evident. While disaster mortality is highest in low-income countries, existing studies focus mostly on developed countries. Here we address this impact attribution question in the context of the Global South using disaster-specific mixed-effects regression models. We show that the rise in landslide and flood mortality in a low-income country such as Nepal between 1992-2021 is primarily attributable to increased precipitation extremes. An increase in one standardized unit in maximum one-day precipitation increases flood mortality by 33%, and heavy rain days increase landslide mortality by 45%. Similarly, a one-unit increase in per capita income decreases landslide and flood mortality by 30% and 45%, respectively. Population density does not show significant effects.

ScenTrees.jl: A Julia Package for Generating Scenario Trees and Scenario Lattices for Multistage Stochastic Programming

Journal of Open Source Software, 2020

Stochastic processes have random and uncertain outcomes. Decisions for stochastic problems involv... more Stochastic processes have random and uncertain outcomes. Decisions for stochastic problems involving such processes must be made at the different stages of the problem. Mathematical problems with such uncertain parameters, described by an underlying probability distribution, are sometimes intractable to solve. For algorithmic treatment, such programs should be approximated by simpler ones, in the same manner as functions are represented as vectors on finite grids on digital computers. In most applications, these underlying distributions are approximated by discrete distributions with a finite number of scenarios, or possible realizations, for the random variables. This approximation procedure is often called scenario generation.

On Dynamic Decomposition of Multistage Stochastic Programs

It is well known that multistage programs, which maximize expectation or expected utility, allow ... more It is well known that multistage programs, which maximize expectation or expected utility, allow a dynamic programming formulation, and that other objectives destroy the dynamic programming character of the problem. This paper considers a risk measure at the final stage of a multistage stochastic program. Although these problems are not time consistent, it is shown that optimal decisions evolve as a martingale. A verification theorem is provided, which characterizes optimal decisions by enveloping sub-and supermartingales. To obtain these characterizations the idea of a constant risk profile has to be given up and instead a risk profile, which varies over time, has to be accepted. The basis of the analysis is a new decomposition theorem for risk measures, which is able to recover the genuine risk measure by measuring risk conditionally.

Climate change and climate insurance. The case of Malawi

IOP Conference Series: Earth and Environmental Science, 2009

This article was submitted without an abstract, please refer to the full-text PDF file.

Time-inconsistent multistage stochastic programs: Martingale bounds

European Journal of Operational Research, 2016

It is well known that multistage programs, which maximize expectation or expected utility, allow ... more It is well known that multistage programs, which maximize expectation or expected utility, allow a dynamic programming formulation, and that other objectives destroy the dynamic programming character of the problem. This paper considers a risk measure at the final stage of a multistage stochastic program. Although these problems are not time consistent, it is shown that optimal decisions evolve as a martingale. A verification theorem is provided, which characterizes optimal decisions by enveloping sub-and supermartingales. To obtain these characterizations the idea of a constant risk profile has to be given up and instead a risk profile, which varies over time, has to be accepted. The basis of the analysis is a new decomposition theorem for risk measures, which is able to recover the genuine risk measure by measuring risk conditionally.

Disaster Risk Transfer for Developing Countries

Financing disaster recovery often diverts resources from development, which can have long-term ef... more Financing disaster recovery often diverts resources from development, which can have long-term effects on economic growth and the poor in developing countries. Moreover, post-disaster assistance, while important for humanitarian reasons, has failed to meet the needs of developing countries in reducing their exposure to disaster risks and assuring sufficient funds to governments and individuals for financing the recovery process. The

Modeling financial disaster risk management in developing countries

The public sector plays a major role in reducing the long-term economic repercussions of disaster... more The public sector plays a major role in reducing the long-term economic repercussions of disasters by repairing damaged infrastructure and providing financial assistance to households and businesses. If critical infrastructure is not repaired in a timely manner, there can be serious effects on the economy and the livelihoods of the population. The repair of public infrastructure, however, can be a

Approximations for Probability Distributions and Stochastic Optimization Problems

International Series in Operations Research & Management Science, 2011

In this chapter, an overview of the scenario generation problem is given. After an introduction, ... more In this chapter, an overview of the scenario generation problem is given. After an introduction, the basic problem of measuring the distance between two single-period probability models is described in Section 15.2. Section 15.3 deals with finding good single-period scenarios based on the results of the first section. The distance concepts are extended to the multi-period situation in Section 15.4. Finally, Section 15.5 deals with the construction and reduction of scenario trees.

A Distance For Multistage Stochastic Optimization Models

SIAM Journal on Optimization, 2012

We describe multistage stochastic programs in a purely in-distribution setting, i.e. without any ... more We describe multistage stochastic programs in a purely in-distribution setting, i.e. without any reference to a concrete probability space. The concept is based on the notion of nested distributions, which encompass in one mathematical object the scenario values as well as the information structure under which decisions have to be made. The nested distance between these distributions is introduced, which turns out to be a generalization of the Wasserstein distance for stochastic two-stage problems. We give characterizations of this distance and show its usefulness in examples. The main result states that the difference of the optimal values of two multistage stochastic programs, which are Lipschitz and differ only in the nested distribution of the stochastic parameters, can be bounded by the nested distance of these distributions. This theorem generalizes the well-known Kantorovich-Rubinstein Theorem, which is applicable only in two-stage situations, to multistage. Moreover, a dual characterization for the nested distance is established. The setup is applicable both for general stochastic processes and for finite scenario trees. In particular, the nested distance between general processes and scenario trees is well defined and becomes the important tool for judging the quality of the scenario tree generation. Minimizing-at least heuristically-this distance is what good scenario tree generation is all about.

Refocusing Disaster Aid

Science, 2005

With new modeling techniques for estimating and pricing the risks of natural disasters, the donor... more With new modeling techniques for estimating and pricing the risks of natural disasters, the donor community is now in a position to help the poor cope with the economic repercussions of disasters by assisting before they happen. Such assistance is possible with the advent of novel insurance instruments for transferring catastrophe risks to the global financial markets. Donor-supported risk-transfer programs not only would leverage limited disaster-aid budgets but also would free recipient countries from depending on the vagaries of postdisaster assistance. Both donors and recipients stand to gain, especially because the instruments can be closely coupled with preventive measures.

Stochastic Dynamic Programming Using Optimal Quantizers

The 1/N investment strategy is optimal under high model ambiguity

Journal of Banking & Finance, 2012

The 1/N investment strategy, i.e. the strategy to split one's wealth uniformly between the availa... more The 1/N investment strategy, i.e. the strategy to split one's wealth uniformly between the available investment possibilities, recently received plenty of attention in the literature. In this paper, we demonstrate that the uniform investment strategy is rational in situations where an agent is faced with a sufficiently high degree of model uncertainty in the form of ambiguous loss distributions. More specifically, we use a classical risk minimization framework to show that, for a broad class of risk measures, as the uncertainty concerning the probabilistic model increases, the optimal decisions tend to the uniform investment strategy. To illustrate the theoretical results of the paper, we investigate the Markowitz portfolio selection model as well as Conditional Value-at-Risk minimization with ambiguous loss distributions. Subsequently, we set up a numerical study using real market data to demonstrate the convergence of optimal portfolio decisions to the uniform investment strategy.

On the Glivenko-Cantelli problem in stochastic programming: Mixed-integer linear recourse

Mathematical Methods of Operations Research, 1998

Expected recourse functions in linear two-stage stochastic programs with mixed-integer second sta... more Expected recourse functions in linear two-stage stochastic programs with mixed-integer second stage are approximated by estimating the underlying probability distribution via empirical measures. Under mild conditions, almost sure uniform convergence of the empirical means to the original expected recourse function is established.

Configurations of series-parallel networks with maximum reliability

Microelectronics Reliability, 1996

The optimal design problem for networks with 3-state components is the following: select from a g... more The optimal design problem for networks with 3-state components is the following: select from a given class of networks with n components, each of which can be operative or experience an open-mode or a shorted-mode failure state, the network with maximum reliability. We present an algorithm for solving this problem in the case of %stage seriesparallel networks, i. e., networks consisting of a number of series configurations linked in parallel or vice versa. For practically relevant network sizes (up to 100 components), the algorithm is fast.

Modelling the Indirect and Fiscal Risks from Natural Disasters Using the CatSim Model

by Reinhard Mechler, Keith Williges, Anna Timonina-Farkas, and Georg Pflug

On Distributionally Robust Multiperiod Stochastic Optimization (joint with G. Pflug)

by Georg Pflug and Bita Analui

The paper considers model uncertainty for multistage stochastic programs. The data and informatio... more The paper considers model uncertainty for multistage stochastic programs. The data and information structure of the baseline model is a tree, on which the decision problem is defined. We consider "ambiguity neighborhoods" around this tree as alternative models which are close to the baseline model. Closeness is defined in terms of a distance for probability trees, called the nested distance. This distance is appropriate for scenario models of multistage stochastic optimization problems as was demonstrated in (Pflug and Pichler, 2012). The ambiguity model is formulated as a minimax problem, where the the optimal decision is to be found, which minimizes the maximal objective function, within the ambiguity set. We give a setup for studying saddle point properties of the minimax problem. Moreover, we present solution algorithms for finding the minimax decisions at least asymptotically. As an example, we consider a multiperiod stochastic production/inventory control problem with weekly ordering. The stochastic scenario process is given by the random demands for two products. We find the worst trees within the ambiguity set and determine a solution which is robust w.r.t. model uncertainty. It turns out that the probability weights of the worst case trees are concentrated on few very bad scenarios.

Pricing of Energy Contracts: From Replication Pricing to Swing Options

by Georg Pflug and Raimund Kovacevic

International Series in Operations Research & Management Science, 2013

Measuring Systemic Risk: Structural Approaches

by Georg Pflug and Raimund Kovacevic

Theory and Practice, 2015

Properties And Computation Of Value At Risk Efficient Portfolios Based On Historical Data

SSRN Electronic Journal, 2000