## Abstract

Uncertainty issues are crucial in assessing the risk posed by natural hazards and developing strategies to mitigate their consequences for society. The challenges are illustrated by the giant earthquake that struck Japan’s Tohoku coast in March, 2011, which was much larger than had been predicted by sophisticated hazard models and so caused a tsunami that overtopped 5–10 m seawalls, causing more than 15,000 deaths and $210 billion damage. Deciding whether to rebuild these defenses and more generally what strategies to employ against such rare events depends on estimating the balance between the costs and benefits of mitigation. Making such estimates is a complex challenge at the intersection of geoscience, mathematics, and economics. The major uncertainty is the probabilities of the rare, extreme events and the waiting or recurrence times between them. The probabilities of these events are difficult to estimate because the physics of earthquake recurrence is not adequately understood, and the short geologic record provides only a few observations. We present a general stochastic model in which the probabilities either are constant with time or depend on the previous history. We then develop models for two hazard policy issues facing Japan. One uses a stochastic model to select an optimum mitigation strategy against future tsunamis by minimizing the sum of the expected present value of the damage, the costs of mitigation, and a risk premium reflecting the variance of the hazard. We also consider whether new nuclear power plants should be built, using a deterministic model that does not require estimating essentially unknown probabilities. These models can be generalized to mitigation policy situations involving other natural hazards.

Original language | English (US) |
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Pages (from-to) | 42-56 |

Number of pages | 15 |

Journal | SIAM-ASA Journal on Uncertainty Quantification |

Volume | 1 |

Issue number | 1 |

DOIs | |

State | Published - 2013 |

## Keywords

- Differential game
- Earthquakes
- Natural hazards
- Optimization
- Stochastic processes
- Tsunami
- Uncertainty

## ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Statistics, Probability and Uncertainty
- Discrete Mathematics and Combinatorics
- Applied Mathematics