The Design of Optimal Insurance Decisions in the Presence of Catastrophic Risks (original) (raw)
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Risk Analysis
As flood risks grow worldwide, a well-designed insurance program engaging various stakeholders becomes a vital instrument in flood risk management. The main challenge concerns the applicability of standard approaches for calculating insurance premiums of rare catastrophic losses. This paper focuses on the design of a flood-loss sharing program involving private insurance based on location-specific exposures. The analysis is guided by developed integrated catastrophe risk management (ICRM) model consisting of GIS-based flood model and a stochastic optimization procedure with respect to location-specific risk exposures. To achieve the stability and robustness of the program towards floods with various recurrences, the ICRM uses stochastic optimization procedure, which relies on quantile-related risk functions of a systemic insolvency involving overpayments and underpayments of the stakeholders. Two alternative ways of calculating insurance premiums are compared: the robust derived with the ICRM and the traditional average annual loss approach. The applicability of the proposed model is illustrated in a case-study of a Rotterdam area outside the main flood protection system in the Netherlands. Our numerical experiments demonstrate essential advantages of the robust premiums, namely that they: 1) guarantee program's solvency under all relevant flood scenarios rather than one average event; 2) establish a tradeoff between the security of the program and the welfare of locations; 3) decrease the need for other risk transfer and risk reduction measures.
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 insurer's 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.
On the Design of Catastrophic Risk Portfolios
1998
Catastrophes produce rare and highly correlated insurance claims, which depend on the amount of coverage at different locations. A joint probability distribution of these claims is analytically intractable. The most promising approach for estimating total claims for a particular combination of decision variables involves geographically explicit simulations of catastrophes. The straightforward use of catastrophe models runs quickly into infinite "if
Natural Catastrophe Models for Insurance Risk Management
2019
Catastrophic events are characterized by three main points: there are relatively rareness, there are statistical unexpected and there have huge impact on the whole society. Insurance or reinsurance is one way of reducing the economic consequences of catastrophic events. Risk management of insurance and reinsurance companies have to have available relevant information for estimation and adjusting premium to cover these risks. The aim of this article is to present two of the useful methods-block maxima method and peaks over threshold method. These methods use information from historical data about insured losses of natural catastrophes and estimates future insured losses. These estimates are very important for actuaries and for risk managers as one of the bases for calculating and adjusting premiums of products covering these types of risks.
Natural catastrophe risk management
Tokovi osiguranja, 2021
Insurance and reinsurance are among the key forms of financial protection against catastrophic events. In modern times, probabilistic models have become increasingly important for assessing the risk of natural disasters, and are used to create insurance and reinsurance services intended to protect citizens, legal entities, as well as the state budget and local governments. Alternative forms of natural catastrophe reinsurance related to the securities market can also significantly help improve the market for (re) insurance against natural catastrophes.
The Role of Financial Instruments in Integrated Catastrophic Flood Management
Multinational Finance Journal, 2003
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 multi-pillar 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 insurance's 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 (JEL G22, G28, C61).
A new approach to modelling claims due to natural hazards
United Nations International Strategy for Disaster Reduction defines risk of natural disaster as "a potentially damaging phenomenon that may lead to loss of life or injury, property damage, social and economic disruption or environmental degradation". Each hazard is characterized by location, intensity, frequency and probability. It is interesting to study inter-arrival time between two disasters in a vulnerable geographic area. In this article, a new approach to model inter-arival time between two disasters based on Stoynov distribution and process is considered. MSC 2010: 60G51, 97K60 1. Introduction. United Nations International Strategy for Disaster Reduction defines risk of natural disaster as "a potentially damaging phenomenon that may lead to loss of life or injury, property damage, social and economic disruption or environmental degradation". Each hazard is characterized by location, intensity, frequency and probability. It is interesting to study inter-a...
Natural Hazards and Earth System Sciences Discussions, 2013
The analysis of flood exposure at a national scale for the French insurance market must combine the generation of a probabilistic event set of all possible (but which have not yet occurred) flood situations with hazard and damage modeling. In this study, hazard and damage models are calibrated on a 1995-2010 historical event set, both for hazard results (river flow, flooded areas) and loss estimations. Thus, uncertainties in the deterministic estimation of a single event loss are known before simulating a probabilistic event set. To take into account at least 90 % of the insured flood losses, the probabilistic event set must combine the river overflow (small and large catchments) with the surface runoff, due to heavy rainfall, on the slopes of the watershed. Indeed, internal studies of the CCR (Caisse Centrale de Reassurance) claim database have shown that approximately 45 % of the insured flood losses are located inside the floodplains and 45 % outside. Another 10 % is due to sea surge floods and groundwater rise. In this approach, two independent probabilistic methods are combined to create a single flood loss distribution: a generation of fictive river flows based on the historical records of the river gauge network and a generation of fictive rain fields on small catchments, calibrated on the 1958-2010 Météo-France rain database SAFRAN. All the events in the probabilistic event sets are simulated with the deterministic model. This hazard and damage distribution is used to simulate the flood losses at the national scale for an insurance company (Macif) and to generate flood areas associated with hazard return periods. The flood maps concern river overflow and surface water runoff. Validation of these maps is conducted by comparison with the address located claim data on a small catchment (downstream Argens).