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In adopting a traditional actuarial view, insurance companies often use expected values to determine the premiums for lifetime health insurance policies with limited coverage, which can lead to serious overpricing problems when the coverage limit is not very low or very high. To address this overpricing problem, this article provides analytical solutions for fair premiums of lifetime health insurance policies with limited coverage. Using internal data provided by insurance companies, this article describes the relationship between the level of limited coverage and excess premiums. The premium difference between a practical pricing method and a proposed pricing model creates a humped curve; the maximum excess premium ratio reaches nearly 20 percent for limited coverage for younger insured people.

This study considers the optimal consumption‐investment‐insurance problem incorporating housing decisions of a household when interest rates and labor income are stochastic. Under the complete market assumption, we derive the closed‐form solution of the optimal insurance demand, portfolio choice, and housing consumption. We calibrate the model using data from the financial market of Taiwan. We find that the insurer's pricing strategy has a significant impact on the household's consumption pattern. Specifically, additional loading in insurance premium allows the life‐cycle model to produce hump‐shaped consumptions of both perishable goods and housing. Loading also creates an unfair background risk to households. However, we only find a small portfolio risk reduction, because households optimally choose a large coverage to mitigate the mortality exposure. This suggests empirical background risk studies overestimate the risk reduction when insurance is available.

We study the relationship between directors’ liability insurance and board meeting attendance. We find that directors’ liability insurance and board meeting attendance are positively associated. This suggests that directors’ liability insurance may actually serve a governance role because an insurer definitely has incentives to thoroughly scrutinize the insured. As a result, director’s board meeting attendance rate increases because more monitoring of directors leads to more responsible behaviors of directors. With 98,524 yearly observations at the director level and 8,968 yearly observations at the firm level of listed firms in Taiwan during the period from 2008 to 2015, our empirical findings suggest that, on average, the board meeting attendance rate of insured firms is 2.9 percent higher than that of uninsured firms.

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