Using Probabilistic Models to Appraise and Decide. Ley-Borrás and Fox

# **Introduction**

The 2005 United Nations World Conference on Disaster Reduction and the resulting Hyogo Framework for Action highlighted the need for pro‐active disaster management, including cost‐effective risk reduction investments and, where this is not possible or as a complement, financial risk transfer through (re)insurance and capital market instrumentation.

Sovereign disaster risk financing and insurance (SDRFI) instruments are among the main resources that states can use for disaster risk reduction (DRR); however, appraising SDRFI instruments can be a challenging task. Deciding on SDRFI instruments requires taking into consideration the different types of disaster risks the state faces; the variety of their economic, social and environmental consequences; and the uncertainty on the occurrence, magnitude, and impact of severe natural events, in addition to the cost, timing, and availability of a wide range of SDRFI instruments.

Probabilistic catastrophe risk models provide a coherent framework for appraising the multiple elements related to SDRFI instruments and they are especially useful for valuing the consequences of uncertain events; it is worth exploring how to get the most value from them.

This paper presents an overview of catastrophe risk models and their use for appraising SDRFI instruments, and suggests a model and a process for improving decision making on sovereign disaster financial instruments. The first section describes probabilistic catastrophe models in terms of their inputs and outputs, and discusses their use by governments to inform sovereign disaster risk financing decision making. The second section describes the financing and insurance instruments available for responding to extreme natural events and the design of strategies that take into consideration the cost and timing of the available financing instruments, in many cases combining ex‐ante and ex‐post instruments. The third section discusses the challenge of appraising SDRFI instruments, including a review of the multiple dimensions of disaster risks; it highlights the value of probabilistic catastrophe risk models for appraising SDRFI instruments. The fourth section puts forward a decision making framework for SDRFI that includes the use of a decision model (an influence diagram) as a rigorous representation of the relationships between the decisions, uncertain events and consequences relevant to SDRFI decision making. The framework also includes a process for generating high quality components for the model (components tailored to the circumstances of the individual country) and a tool for designing coherent SDRFI strategies. Finally, suggestions for enriching catastrophe risk models in order to facilitate SDRFI decision making are presented.

# **1. Probabilistic Catastrophe Models**

Catastrophe risk models have been developed and used by participants in the private international (re)insurance community since the late 1980s. Functionally, these models attempt to represent the likely direct economic impact of natural hazards (e.g., hurricanes) on a portfolio of physical assets at risks (e.g., a selection of hotels in Miami) and provide outputs that can be used by decision makers to inform their risk management strategies. There are two distinct types of catastrophe modeling analysis that can be performed: deterministic and probabilistic. Deterministic (or "what if") analyses represent the impact of

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