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Hundreds of billions of dollars have been spent in homeland security since September 11, 2001. Many mathematical models have been developed to study strategic interactions between governments (defenders) and terrorists (attackers). However, few studies have considered the tradeoff between equity and efficiency in homeland security resource allocation. In this article, we fill this gap by developing a novel model in which a government allocates defensive resources among multiple potential targets, while reserving a portion of defensive resources (represented by the equity coefficient) for equal distribution (according to geographical areas, population, density, etc.). Such a way to model equity is one of many alternatives, but was directly inspired by homeland security resource allocation practice. The government is faced with a strategic terrorist (adaptive adversary) whose attack probabilities are endogenously determined in the model. We study the effect of the equity coefficient on the optimal defensive resource allocations and the corresponding expected loss. We find that the cost of equity (in terms of increased expected loss) increases convexly in the equity coefficient. Furthermore, such cost is lower when: (a) government uses per-valuation equity; (b) the cost-effectiveness coefficient of defense increases; and (c) the total defense budget increases. Our model, results, and insights could be used to assist policy making.

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The current system for managing natural disaster risk in the United States is problematic for both homeowners and insurers. Homeowners are often uninsured or underinsured against natural disaster losses, and typically do not invest in retrofits that can reduce losses. Insurers often do not want to insure against these losses, which are some of their biggest exposures and can cause an undesirably high chance of insolvency. There is a need to design an improved system that acknowledges the different perspectives of the stakeholders. In this article, we introduce a new modeling framework to help understand and manage the insurer's role in catastrophe risk management. The framework includes a new game-theoretic optimization model of insurer decisions that interacts with a utility-based homeowner decision model and is integrated with a regional catastrophe loss estimation model. Reinsurer and government roles are represented as bounds on the insurer-insured interactions. We demonstrate the model for a full-scale case study for hurricane risk to residential buildings in eastern North Carolina; present the results from the perspectives of all stakeholders-primary insurers, homeowners (insured and uninsured), and reinsurers; and examine the effect of key parameters on the results.

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