Design of Flood-loss Sharing Programs in the Upper Tisza Region, Hungary: A dynamic multi-agent adaptive Monte Carlo approach

Losses from human-made and natural catastrophes are rapidly increasing. The main reason for this is the clustering of people and capital in hazard-prone areas as well as the creation of new hazard-prone areas, a phenomenon that may be aggravated by a lack of knowledge of the risks. This alarming human-induced tendency calls for new integrated approaches to catastrophic risk management. This paper demonstrates how flood catastrophe model and adaptive Monte Carlo optimization can be linked into an integrated Catastrophe Management Model to give insights on the feasibility of a flood management program and to assist in designing a robust program. As a part of integrated flood risk management, the proposed model takes into account the specifics of the catastrophic risk management: highly mutually dependent losses, the lack of information, the need for long-term perspectives and geographically explicit models, the involvement of various agents such as individuals, governments, insurers, reinsurers, and investors. Therefore, the integrated catastrophe management model turns out to be an important mitigation measure in comprehending catastrophes. As a concrete case we consider a pilot region of the Upper Tisza river, Hungary. Specifically, we analyze the demand of the region in a multipillar flood-loss sharing program involving a partial compensation by the central government, a voluntary private property insurance, a voluntary private risk-based insurance GIS-based catastrophe models and specific stochastic optimization methods are used to guide policy analysis with respect to location-specific risk exposures. To analyze the stability of the program, we use economically sound risk indicators

Integrated Modeling of Spatial and Temporal Heterogeneities and Decisions Induced by Catastrophic Events

This paper discusses an integrated model capable of dealing with spatial and temporal heterogeneities induced by extreme events, in particular weather related catastrophes. The model can be used for quite different problems which take explicitly into account the specifics of catastrophic risks: highly mutually dependent losses, inherent capacity of information, the need for long-term perspectives (temporal heterogeneity) and geographically explicit analyses (spatial heterogeneity) with respect to losses and gains of various agents such as individuals, governments, farmers, products, consumers, insurers, investors, and their decisions on coping with risks. We illustrate emerging challenging decision-making problems with a case study of severe floods in a pilot region in the Upper Tisza River. Special attention is given to the evaluation of a flood loss-spreading program taking explicitly into account location specific distributions of agricultural and structural losses. This enables us to evaluate premiums, insurance coverage, and governmental compensation schemes minimizing, in a sense, the risk of locations to overpay actual losses, risks of bankruptcy/insolvency for insurers, and overcompensation of losses by the government. GIS-based catastrophe models and stochastic optimization methods are used to guide policy analysis with respect to location-specific risk exposures. We use special risk functions in order to convexity discontinuous insolvency constrains

Optimization of Social Security Systems Under Uncertainty

The aim of this paper is to develop optimization-based approaches for modeling multi-agent and multi-regional social security systems under demographic and economic uncertainties. Conceptually, the proposed model deals with the production and consumption processes coevolving with "birth-and-death" processes of the participating agents. Uncertainties concern fertility, life expectancy, migration and such economic and health variables as rate of return, incomes and disability rates. The goal is to satisfy a reasonable and secure consumption of agents. There is considerable similarity between the decisions involved in the optimization of social security systems and the production planning processes: in both cases "savings" are taken in periods of low demand and "dissavings" when the demand turns high. The significant difference of our problem is that decisions on savings and dissavings may have large-scale effects on the whole economy, in particular, they effect returns on savings through investments and capital formation. The model tracks incomes and expenditures of agents, their savings and dissavings, as well as intergenerational and interregional transfers of wealth. Robust management strategies are defined by using such risk indicators as ruin, shortfall and Conditional-Value-at-Risk (CVaR). The adaptive Monte Carlo optimization procedure is proposed to derive optimal decisions. Numerical experiments and possible applications to catastrophic risk management are discussed

Global Changes: Facets of Robust Decisions

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 of global changes. Unlike statistical robustness, general decision problems may have rather different facets of robustness. In particular, a key issue is the sensitivity 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

The role of financial instruments in integrated catastrophic flood management

The main goal of this paper is to develop a flood management model that takes into account the specifics of catastrophic risk management: highly mutually dependent losses, the lack of information, the need for long-term perspectives and explicit analyses of spatial and temporal heterogeneities of various agents such as individuals, governments, and insurers. We use modified data from a pilot region of the Upper Tisza river, Hungary, to illustrate the evaluation of a public multipillar flood loss-spreading program involving partial compensation to flood victims by the central government, the pooling of risks through a mandatory public catastrophe insurance on the basis of location-specific exposures, and the demand for a contingent ex-ante credit to reinsure the insurances liabilities. GIS-based catastrophe models and stochastic optimization methods are used to guide policy analysis with respect to location-specific risk exposures. We use economically sound risk indicators leading to convex stochastic optimization problems strongly connected with nonconvex insolvency constraint, VaR and CVaR

A Systems Approach to Management of Catastrophic Risks

There are two main strategies in dealing with rare and dependent catastrophic risks: the use of risk reduction measures (preparedness programs, land-use regulations, etc.) and the use of risk-spreading mechanisms, such as insurance and financial markets. These strategies are not separable. The risk reduction measures increase the insurability of risks. On the other hand, the insurance policies on premiums may enforce risk reduction measures. The role of system approaches, models and accompanying decision support systems becomes of critical importance for managing catastrophic risks. The paper discusses some methodological challenges concerning the design of such models and decision support systems

Allocation of Resources for Protecting Public Goods against Uncertain Threats Generated by Agents

This paper analyses a framework for designing robust decisions against uncertain threats to public goods generated by multiple agents. The agents can be intentional attackers such as terrorists, agents accumulating values in flood or earthquake prone locations, or agents generating extreme events such as electricity outage and recent BP oil spill, etc. Instead of using a leader-follower game theoretic framework, this paper proposes a decision theoretic model based on two-stage stochastic optimization (STO) models for advising optimal resource allocations (or regulations) in situations characterized by uncertain perceptions of agent behaviors. In particular, the stochastic mini-max model and multi- shortfalls) is advanced in the context of quantile optimization for dealing with potential extreme events. Proposed framework can deal with both direct and indirect judgments on the decision makers perception about uncertain agent behaviors, either directly by probability density estimation, or indirectly by probabilistic inversion. The quantified distributions are treated as input to the stochastic optimization models in order to address inherent uncertainties. Robust decisions can then be obtained against all possible threats, especially with extreme consequences. This paper also introduces and compares three different computational algorithms which can be used to solve arising two-stage STO problems, including bilateral descent method, linear programming approximation and stochastic quasi-gradient method. A numerical example of high dimensionlity is presented for illustration of their performance under large number of scenarios typically required for dealing with low probability extreme events. Case studies include deensive resource allocations among cities and security of electricity networks

Risk, Security and Robust Solutions

The aim of this paper is to develop a decision-theoretic approach to security management of uncertain multi-agent systems. Security is defined as the ability to deal with intentional and unintentional threats generated by agents. The main concern of the paper is the protection of public goods from these threats allowing explicit treatment of inherent uncertainties and robust security management solutions. The paper shows that robust solutions can be properly designed by new stochastic optimization tools applicable for multicriteria problems with uncertain probability distributions and multivariate extreme events