T. Ermolieva

Stochastic Optimization of Insurance Portfolios for Managing Exposure to Catastrophic Risks

A catastrophe may affect different locations and produce losses that are rare and highly correlated in space and time. It may ruin many insurers if their risk exposures are not properly diversified among locations. The multidimentional distribution of claims from different locations depends on decision variables such as the insurers coverage at different locations, on spatial and temporal characteristics of possible catastrophes and the vulnerability of insured values. As this distribution is analytically intractable, the most promising approach for managing the exposure of insurance portfolios to catastrophic risks requires geographically explicit simulations of catastrophes. The straightforward use of so-called catastrophe modeling runs quickly into an extremely large number of “what-if” evaluations. The aim of this paper is to develop an approach that integrates catastrophe modeling with stochastic optimization techniques to support decision making on coverages of losses, profits, stability, and survival of insurers. We establish connections between ruin probability and the maximization of concave risk functions and we outline numerical experiments.

A system 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.

A Systems Approach to Modeling Catastrophic Risk and Insurability

This paper describes a spatial-dynamic,stochastic optimization model that takes account ofthe complexities and dependencies of catastrophicrisks. Following a description of the general model,the paper briefly discusses a case study of earthquakerisk in the Irkutsk region of Russia. For this purposethe risk management model is customized to explicitlyincorporate the geological characteristics of theregion, as well as the seismic hazards and thevulnerability of the built environment. In its generalform, the model can analyze the interplay betweeninvestment in mitigation and risk-sharing measures. Inthe application described in this paper, the modelgenerates insurance strategies that are lessvulnerable to insolvency.

Biofuel development, food security and the use of marginal land in China.

With concerns of energy shortages, China, like the United States, European Union, and other countries, is promoting the development of biofuels. However, China also faces high future demand for food and feed, and so its bioenergy program must try to strike a balance between food and fuel. The goals of this paper are to provide an overview of Chinas current bioethanol program, identify the potential for using marginal lands for feedstock production, and measure the likely impacts of Chinas bioethanol development on the nations future food self-sufficiency. Our results indicate that the potential to use marginal land for bioethanol feedstock production is limited. Applying a modeling approach based on highly disaggregated data by region, our analysis shows that the target of 10 million t of bioethanol by 2020 seems to be a prudent target, causing no major disturbances in Chinas food security. But the expansion of bioethanol may increase environmental pressures due to the higher levels of fertilizer use. This study shows also that if China were able to cultivate 45% of its required bioethanol feedstock on new marginal land, it would further limit negative effects of the bioethanol program on the domestic and international economy, but at the expense of having to apply another 750 thousand t of fertilizer.

Insurability of catastrophic risks: The stochastic optimization model

Catastrophes produce losses highly correlated in space and time, which break the law of large numbers. We derive the insurability of dependent catastrophic risks by calculating conditions that would aid insurers in deliberate selection of their portfolios. This paper outlines the general structure of a basic stochastic optimization model. Connections between the probability of ruin and nonsmooth risk functions, as well as adaptive Monte Carlo optimization procedures and path dependent laws of large numbers, are discussed

Endogenous Risks and Learning in Climate Change Decision Analysis

We analyze the effects of risks and learning on climate change decisions. Using a new two-stage, dynamic, climate change stabilization model with random time horizons, we show that the explicit incorporation of ex-post learning and safety constraints induces risk aversion in ex-ante decisions. This risk aversion takes the form in linear models of VaR- and CVaR-type risk measures. We also analyze extensions of the model that account for the possibility of nonlinear costs, limited emissions abatement capacity, and partial learning. We find that in all cases, even in linear models, any conclusion about the effect of learning can be reversed. Namely, learning may lead to either less- or more restrictive ex-ante emission reductions depending on model assumptions regarding costs, the distributions describing uncertainties, and assumptions about what might be learned. We analyze stylized elements of the model in order to identify the key factors driving outcomes and conclude that, unlike in most previous models, the quantiles of probability distributions play a critical role in solutions.

Energy efficiency and risk management in public buildings: strategic model for robust planning

Due to deregulations of the energy sector and the setting of targets such as the 20/20/20 in the EU, operators of public buildings are now more exposed to instantaneous (short-term) market conditions. On the other hand, they have gained the opportunity to play a more active role in securing long-term supply, managing demand, and hedging against risk while improving existing buildings’ infrastructures. Therefore, there are incentives for the operators to develop and use a Decision Support System to manage their energy sub-systems in a more robust energy-efficient and cost-effective manner. In this paper, a two-stage stochastic model is proposed, where some decisions (so-called first-stage decisions) regarding investments in new energy technologies have to be taken before uncertainties are resolved, and some others (so-called second-stage decisions) on how to use the installed technologies will be taken once values for uncertain parameters become known, thereby providing a trade-off between long- and short-term decisions.

Simulation-based optimization of social security systems under uncertainty

This paper analyzes optimization-based approaches for a social security simulation model under demographic and economic uncertainties. The model is a compromise between a purely actuarial model and an overlapping generations general equilibrium model. It deals with production and consumption processes coevolving with “birth-and-death” processes of involved agents, e.g., region-specific households subdivided into single-year age groups, firms, governments, financial intermediaries, including pension systems and insurance. The production function of the model allows to track incomes expenditures, savings and dissavings of agents, as well as intergenerational and interregional transfers of wealth. The proposed approach combines the actuarial and the economic growth simulation models in a single stochastic optimization model which explicitly and realistically treats the underlying uncertainties with the goal to satisfy reasonable and secure consumption of agents. The design of optimal robust strategies is achieved by an adaptive simulation-based optimization procedure defined by non-smooth risk functions. Numerical solution is discussed.

Discounting, catastrophic risks management and vulnerability modeling

Traditional discounting dramatically affects the outcome of catastrophic risk management and spatio-temporal vulnerability modeling. The misperception of discount rates produces inadequate evaluations of risk management strategies, which may provoke catastrophes and significantly contribute to the increasing vulnerability of our society. This paper analyses the implication of potential catastrophic events on the choice of discounting. In particular, it shows the necessity of using proposed equivalent undiscounted stopping time criterion and Monte Carlo based stochastic optimization procedures.

Integrated Catastrophe Risk Modeling: Supporting Policy Processes

Efficient and equitable policies for managing disaster risks and adapting to global environmental change are critically dependent on development of robust options supported by integrated modeling. The book is based on research and state-of-the art models developed at IIASA (International Institute for Applied Systems Analysis) and within its cooperation network. It addresses the methodological complexities of assessing disaster risks, which call for stochastic simulation, optimization methods and economic modeling. Furthermore, it describes policy frameworks for integrated disaster risk management, including stakeholder participation facilitated by user-interactive decision-support tools. Applications and results are presented for a number of case studies at different problem scales and in different socio-economic contexts, and their implications for loss sharing policies and economic development are discussed. Among others, the book presents studies for insurance policies for earthquakes in the Tuscany region in Italy and flood risk in the Tisza river basin in Hungary. Further, it investigates the economic impact of natural disasters on development and possible financial coping strategies; and applications are shown for selected South Asian countries. The book is addressed both to researchers and to organizations involved with catastrophe risk management and risk mitigation policies.