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As the cyber insurance market is expanding and cyber insurance policies continue to mature, the potential of including pre-incident and post-incident services into cyber policies is being recognised by insurers and insurance buyers. This work addresses the question of how such services should be priced from the insurer's viewpoint, i.e. under which conditions it is rational for a profit-maximising, risk-neutral or risk-averse insurer to share the costs of providing risk mitigation services. The interaction between insurance buyer and seller is modelled as a Stackelberg game, where both parties use distortion risk measures to model their individual risk aversion. After linking the notions of pre-incident and post-incident services to the concepts of self-protection and self-insurance, we show that when pricing a single contract, the insurer would always shift the full cost of self-protection services to the insured; however, this does not generally hold for the pricing of self-insurance services or when taking a portfolio viewpoint. We illustrate the latter statement using toy examples of risks with dependence mechanisms representative in the cyber context. Supplementary Information: The online version contains supplementary material available at 10.1057/s41288-023-00289-7.

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Parity in coverage for mental health services has been a longstanding policy aim at the state and federal levels and is a regulatory feature of the Affordable Care Act. Despite the importance and legislative effort involved in these policies, evaluations of their effects on patients yield mixed results. I leverage the Employee Retirement Income Security Act and unique claims-level data that includes information on employers' self-insurance status to shed new light in this area after the implementation of two state parity laws in 2007 and federal parity a few years later. My empirics reveal evidence of strategic avoidance on behalf of insurers in both states prior to the passage of state parity, as well as positive increases in mental health care utilization after parity laws are implemented - but context matters. Policy heterogeneity across states and strategic behaviors by employers and commercial insurers substantively shape the benefits that ultimately flow to patients. Insights from this research have broad relevance to ongoing health policy debates, particularly as states retain great discretion over many health coverage decisions and as federal policy continues to evolve.

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Several factors are at work. Group health insurance got more expensive when the ACA mandated essential health benefits and no-cost preventive care. Some small companies dropped coverage altogether, but now they are coming back into the fold as the employment market has tightened up, say brokers. Starting fresh, they have a chance to consider self-insurance.

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The Affordable Care Act (ACA) imposes adjusted community rating in the small group market, which employers can avoid by self-insuring, raising concerns about adverse selection. We evaluate the impact of limiting allowable rating variation on employer self-insurance across industries with varied health risk, using cross-state variation in pre-ACA rating regulations, the nationally-representative 2008-2013 KFF/HRET Employer Health Benefits survey, and a triple-difference regression approach. We find that lower-risk employers subject to laws limiting allowable premium rating variation have a predicted probability of self-insurance that is about 18 percentage points higher than otherwise-similar higher-risk employers, suggesting that these selection concerns are warranted.