The Design of Optimal Insurance Decisions in the Presence of Catastrophic Risks

This paper deals with the development of decision making tools for managing catastrophic (low probability - high consequences) risks. Catastrophes produce rare and highly correlated claims, which depend on various decision variables, i.e., coverages at different locations, mitigation measures and reinsurance agreements. Joint probability distributions of these claims depicting their complex spatial and temporal interactions and effects of decision variables are analytically intractable. Spatial stochastic models of catastrophes can bypass these difficulties. Catastrophic models combine the simulation of realistic and geographically explicit catastrophic events with the differentiation of property values and insurance coverages in different locations of the region. Catastrophic models can be combined with stochastic optimization techniques to aid decision making on the spatial diversification of contracts, insurance premiums, reinsurance requirements, effects of mitigation measures, and the use of other financial mechanisms. The aim of this paper is to extend a two-stage spatial catastrophic model to dynamic cases reflecting dependencies of risk accumulation processes in time. This extension is important since it can be used for the analysis of decisions under changing frequencies of events and values of properties. It is also possible to incorporate catastrophes caused by the clustering in time of such events as rains and droughts due to persistence in climate. The model can be used by individual insurers, pools of insurers or regulatory authorities

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

Abrupt Climate Change: Lessons from Integrated Catastrophic Risk Management

This paper is an extended version of the talks "Uncertainty and Robust Solutions: Lessons from IIASA Case Studies on Catastrophic Risk Management and Economic Growth under Shocks" given on 12 June 2002 and "Sink Technologies and Climate Risk Management" given on 15 May 2002 at IIASA's Greenhouse Gas Initiative seminars (see web site: www.iiasa.ac.at/~marek/ggi/). Risks of disaster arise out of the combination of natural hazards and human activities. We argue that by divorcing the natural disaster issues from social and economic development, half of this disaster equation is ignored. The current pace of disaster development is undermining the markets and safety nets not only of developing countries. Far greater policy coherence is needed between economists, development planners, natural scientists and disaster managers in order to prevent catastrophic losses to human lives, livelihoods, and natural and economic assets. In this paper we present an integrated approach to catastrophic risk management that aims at more coherence and comprehensiveness. The models presented take into account spatial and temporal heterogeneity of catastrophes as well as institutional heterogeneity within a model of economic growth. Loss and gains profiles are functions of various strategies/requirements/goals of agents such as individuals, governments, producers, insurers and investors. GIS-based catastrophe models and stochastic optimization methods allow to guide policy analyses with respect to location specific risk exposures

Spatial Stochastic Model for Optimization Capacity of Insurance Networks Under Dependent Catastrophic Risks: Numerical Experiments

The paper proposes for the general framework for the optimization capacity of an insurance industry in responding to catastrophic risks. Explicit geographical representation allows for sufficient differentiation of property values and insurance coverages in different parts of the region and for realistic modeling of catastrophes in space and time. Numerical experiments demonstrate the possibility of stochastic optimization techniques for optimal diversification of catastrophic exposure. This is important for increasing the stability of insurers, their profits and for the financial protection of the population

Modeling Earthquakes via Computer Programs

Modeling earthquakes plays an important role in investigation of different aspects of seismic risk. The paper continues previous studies and describes the user-friendly software destined for numerical simulation of lithosphere dynamics and seismicity by means of different modifications of the block model, which exploits the hierarchical block structure of the lithosphere. As a result, the model produces an earthquake catalog, and the programs give an opportunity to visualize it in different ways. The programs work in an interactive mode with a window interface. Numerical approximation of the Vrancea seismic region is considered as an example of application of the software. Parallel algorithms allowing to perform modeling dynamics of rather large structures are outlined

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

Earthquake Risk Management: A Scenario Generator

This paper presents a software package EDGE, an Earthquake Damage Generator/Estimator for Toscana, Italy. EDGE creates samples of multidimentional distributions of damage using models of geophysical processes, seismic-geophysical data and a catalog of vulnerability of buildings in the region. The main algorithmic elements: seismic maps, geophysical formulas, and stochastic modeling, are described in detail. The work contributes to a joint research program of Dynamic Systems, and Risk, Modeling and Society projects on data-based methodological support for decision making in the insurance industry against risks of natural catastrophes. The designed catalogs of expected damages can be used for actuarial calculations and optimization of the regional insurance portfolio

Induced Discounting and Its Implications to Catastrophic Risk Management

The implication of risks for justifying long-term investment remains a controversial issue. For example, how can we justify mitigation efforts for a 200-year flood that may, in fact, occur in one year or in 300 years? Discount rates obtained from capital markets are linked to assets with lifespans of a few decades and, as such, may significantly underestimate the results of long-term mitigations. In this paper, we show that the explicit treatment of extreme catastrophic events and related uncertain time horizons and risks induce dynamically adjusted discount rates, conditional on the degree of social commitment to mitigate risk. In particular, the standard time geometric (exponential) discount factors are induced by an event with time horizons characterized by a "memoryless" geometric (exponential) probability distribution. A set of such events induces declining time inconsistent discount rates that are dominated by least probable extreme events. In general, risk affects discount rates, which alter the optimal mitigation efforts that in turn, change the risk. We show that the induced discount factors can be analyzed by solving stochastic optimization problems. Our simulation results indicate that the misperception of time inconsistency associated with induced discounting may dramatically effect - delay or provoke - the possibility of catastrophic collapse

Uncertainty and Disaster Risk Management: Modeling the Flash Flood Risk to Vienna and Its Subway System

This report describes an interdisciplinary approach to flood risk analysis and management that was developed by investigating flood risks in the city of Vienna, Austria. The purpose of the research was to analyze different policy paths (including both flood-prevention measures and risk-sharing financial provisions) in the presence of major uncertainties. A preliminary analysis resulted in the identification of two major methodological issues that needed to be resolved, namely: -- The concept of risk used in flood management varied subtly but significantly across the disciplines contributing to the assessment. -- Current assessment procedures did not give a full account of uncertainties and their different types. For those reasons an approach was developed that allows the analyst: (1) to integrate the different diciplinary concepts of risk within a single interdisciplinary analysis; and (2) to take into account uncertainties in a way that not only allows their many characteristics to be distinguished but is also consistent across the component disciplines. The focus of this report is the phenomenon of flash flooing of the Vienna River. Our analysis demonstrated that, in this case, the greatest damage from flash flooding was to be expected in the Vienna city subway system. The report thus describes a detailed assessment of the flood risk to the subway and of related management measures, on which research to date has been scarce. The results show that an approach based on catastrophe modeling and Monte Carlo simulation can not ony integrate the risk perspectives of the different technical disciplines contributing to this study but also provide a useful framework for comparing the characteristics of different mitigation strategies. The results of the simulations suggest alternatives for combining different mitigation measures to ensure complementarity among the characteristics of different components of an overall strategy, and thereby decrease total costs and reduce the likelihood and the uncertainties of catastrophic financial losses

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