We develop a computational framework for the stochastic and dynamic modeling of regional natural catastrophe losses with an insurance industry to support government decision‐making for hurricane risk management. The analysis captures the temporal changes in the building inventory due to the acquisition (buyouts) of high‐risk properties and the vulnerability of the building stock due to retrofit mitigation decisions. The system is comprised of a set of interacting models to (1) simulate hazard events; (2) estimate regional hurricane‐induced losses from each hazard event based on an evolving building inventory; (3) capture acquisition offer acceptance, retrofit implementation, and insurance purchase behaviors of homeowners; and (4) represent an insurance market sensitive to demand with strategically interrelated primary insurers. This framework is linked to a simulation‐optimization model to optimize decision‐making by a government entity whose objective is to minimize region‐wide hurricane losses. We examine the effect of different policies on homeowner mitigation, insurance take‐up rate, insurer profit, and solvency in a case study using data for eastern North Carolina. Our findings indicate that an approach that coordinates insurance, retrofits, and acquisition of high‐risk properties effectively reduces total (uninsured and insured) losses.
Effective Premium Discrimination for Designing Cyber Insurance Policies with Rare Losses
Cyber insurance like other types of insurance is a method of risk transfer, where the insured pays a premium in exchange for coverage in the event of a loss. As a result of the reduced risk for the insured and the lack of information on the insurer’s side, the insured is generally inclined to lower its effort, leading to a worse state of security, a common phenomenon known as moral hazard. To mitigate moral hazard, a widely employed concept is premium discrimination, i.e., an agent/insured who exerts higher effort pays less premium. This, however, relies on the insurer’s ability to assess the effort exerted by the insured. In this paper, we study two methods of premium discrimination that rely on two different types of assessment: pre-screening and post-screening. Pre-screening occurs before the insured enters into a contract and can be done at the beginning of each contract period; the result of this process gives the insurer an estimated risk on the insured, which then determines the contract terms. The post-screening mechanism involves at least two contract periods whereby the second-period premium is increased if a loss event occurs during the first period.
Prior work shows that both pre-screening and post-screening are generally effective in mitigating moral hazard and increasing the insured’s effort. The analysis in this study shows, however, that the conclusion becomes more nuanced when loss events are rare. Specifically, we show that post-screening is not effective at all with rare losses, while pre-screening can be an effective method when the agent perceives them as rarer than the insurer does; in this case pre-screening improves both the agent’s effort level and the insurer’s profit.
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- Award ID(s):
- 1739517
- NSF-PAR ID:
- 10202977
- Date Published:
- Journal Name:
- Conference on Decision and Game Theory for Security (GameSec)
- Page Range / eLocation ID:
- 259-275
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract -
We study the problem of designing cyber insurance policies in an interdependent network, where the loss of one agent (a primary party) depends not only on his own effort, but also on the investments and efforts of others (third parties) in the same eco-system (i.e., externalities). In designing cyber insurance policies, the conventional wisdom is to avoid insuring dependent parties for two reasons. First, simultaneous loss incidents threaten the insurer's business and capital. Second, when a loss incident can be attributed to a third party, the insurer of the primary party can get compensation from the insurer of the third party in order to reduce its own risk exposure. In this work, we analyze an interdependent network model in order to understand whether an insurer should avoid or embrace risks interdependencies. We focus on two interdependent agents, where the risk of one agent (primary party) depends on the other agent (third party), but not the other way around. We consider two potential scenarios: one in which an insurer only insures a primary party, and another one in which the insurer of the primary party further insures the third party agent. We show that it is in fact profitable for the primary party's insurer to insure both agents. Further, we show that insuring both agents not only provides higher profit for the insurer, but also reduces the collective risk.more » « less
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Abstract Flooding causes more damage and severely impacts more people worldwide than any other natural disaster. Flood risk in many parts of the United States is projected to increase due to both continued floodplain development and climate change. Many of our institutions and public policies are not designed to address these changing risk conditions. The practice of grandfathering insurance premiums in the National Flood Insurance Program (NFIP)—allowing an insured to keep a lower rate even when risk has increased—is one such policy. We link a flood hazard model to a flood insurance premium calculator in order to provide illustrative calculations of the possible impact of grandfathering on program revenue and policyholder premiums due to sea level rise for a New York City neighborhood. We conclude by discussing how to preserve the financial soundness of the NFIP while addressing the affordability of insurance in the face of increasing flood risk.
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The actuarially fair insurance premium reflects the expected loss for each insured. Given the dearth of cyber security loss data, market premiums could shed light on the true magnitude of cyber losses despite noise from factors unrelated to losses. To that end, we extract cyber insurance pricing information from the regulatory filings of 26 insurers. We provide empirical observations on how premiums vary by coverage type, amount, policyholder type, and over time. A method using Particle Swarm Optimization is introduced to iterate through candidate parameterized distributions with the goal of reducing error in predicting observed prices. We then aggregate the inferred loss models across 6,828 observed prices from all 26 insurers to derive the County Fair Cyber Loss Distribution. We demonstrate its value in decision support by applying it to a theoretical retail firm with annual revenue of $50M. The results suggest that the expected cyber liability loss is $428K, and that the firm faces a 2.3%chance of experiencing a cyber liability loss between $100K and $10M each year. The method could help organizations better manage cyber risk, regardless of whether they purchase insurance.more » « less
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null (Ed.)Insurance premiums reflect expectations about the future losses of each insured. Given the dearth of cyber security loss data, market premiums could shed light on the true magnitude of cyber losses despite noise from factors unrelated to losses. To that end, we extract cyber insurance pricing information from the regulatory filings of 26 insurers. We provide empirical observations on how premiums vary by coverage type, amount, and policyholder type and over time. A method using particle swarm optimisation and the expected value premium principle is introduced to iterate through candidate parameterised distributions with the goal of reducing error in predicting observed prices. We then aggregate the inferred loss models across 6,828 observed prices from all 26 insurers to derive the County Fair Cyber Loss Distribution . We demonstrate its value in decision support by applying it to a theoretical retail firm with annual revenue of $50M. The results suggest that the expected cyber liability loss is $428K and that the firm faces a 2.3% chance of experiencing a cyber liability loss between $100K and $10M each year. The method and resulting estimates could help organisations better manage cyber risk, regardless of whether they purchase insurance.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-32430-8_16
