skip to main content

Title: 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 more » 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. « less
Authors:
; ;
Award ID(s):
1739517
Publication Date:
NSF-PAR ID:
10202977
Journal Name:
Conference on Decision and Game Theory for Security (GameSec)
Page Range or eLocation-ID:
259-275
Sponsoring Org:
National Science Foundation
More Like this
  1. We consider a game in which one player (the principal) seeks to incentivize another player (the agent) to exert effort that is costly to the agent. Any effort exerted leads to an outcome that is a stochastic function of the effort. The amount of effort exerted by the agent is private information for the agent and the principal observes only the outcome; thus, the agent can misreport his effort to gain higher payment. Further, the cost function of the agent is also unknown to the principal and the agent can also misreport a higher cost function to gain higher paymentmore »for the same effort. We pose the problem as one of contract design when both adverse selection and moral hazard are present. We show that if the principal and agent interact only finitely many times, it is always possible for the agent to lie due to the asymmetric information pattern and claim a higher payment than if he were unable to lie. However, if the principal and agent interact infinitely many times, then the principal can utilize the observed outcomes to update the contract in a manner that reveals the private cost function of the agent and hence leads to the agent not being able to derive any rent. The result can also be interpreted as saying that the agent is unable to keep his information private if he interacts with the principal sufficiently often.« less
  2. 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 themore »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.« less
  3. 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 predictingmore »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.« less
  4. This article deals with household-level flood risk mitigation. We present an agent-based modeling framework to simulate the mechanism of natural hazard and human interactions, to allow evaluation of community flood risk, and to predict various adaptation outcomes. The framework considers each household as an autonomous, yet socially connected, agent. A Beta-Bernoulli Bayesian learning model is first applied to measure changes of agents' risk perceptions in response to stochastic storm surges. Then the risk appraisal behaviors of agents, as a function of willingness-to-pay for flood insurance, are measured. Using Miami-Dade County, Florida as a case study, we simulated four scenarios tomore »evaluate the outcomes of alternative adaptation strategies. Results show that community damage decreases significantly after a few years when agents become cognizant of flood risks. Compared to insurance policies with pre-Flood Insurance Rate Maps subsidies, risk-based insurance policies are more effective in promoting community resilience, but it will decrease motivations to purchase flood insurance, especially for households outside of high-risk areas. We evaluated vital model parameters using a local sensitivity analysis. Simulation results demonstrate the importance of an integrated adaptation strategy in community flood risk management.« less
  5. We investigate how sequential decision making analysis can be used for modeling system resilience. In the aftermath of an extreme event, agents involved in the emergency management aim at an optimal recovery process, trading off the loss due to lack of system functionality with the investment needed for a fast recovery. This process can be formulated as a sequential decision-making optimization problem, where the overall loss has to be minimized by adopting an appropriate policy, and dynamic programming applied to Markov Decision Processes (MDPs) provides a rational and computationally feasible framework for a quantitative analysis. The paper investigates how trendsmore »of post-event loss and recovery can be understood in light of the sequential decision making framework. Specifically, it is well known that system’s functionality is often taken to a level different from that before the event: this can be the result of budget constraints and/or economic opportunity, and the framework has the potential of integrating these considerations. But we focus on the specific case of an agent learning something new about the process, and reacting by updating the target functionality level of the system. We illustrate how this can happen in a simplified setting, by using Hidden-Model MPDs (HM-MDPs) for modelling the management of a set of components under model uncertainty. When an extreme event occurs, the agent updates the hazard model and, consequently, her response and long-term planning.« less