Pricing for Multiline Insurer: Frictional Costs, Insolvency, and Asset Allocation

This article examines multiline insurance pricing based on the contingent claim approach in a limited liability and frictional costs environment. Capital allocation is based on the value of the default option, which satisfies the realistic assumption that each distinct line undertakes a pro rata share of deficit caused by insurer insolvency. Premium levels, available assets, and default risk interact with each other and reach equilibrium at the fair premium. The assets available to pay for liabilities are not predetermined or given; instead, the premium income and investment income jointly influence the available assets. The results show that equity allocation does not influence the overall fair premium. For a given expected loss, the premium‐to‐expected‐loss ratio for firms offering multiple lines is higher than that for firms only offering a single line, due to the reduced risk achieved through diversification. Premium‐to‐expected‐loss ratio and equity‐to‐expected‐loss ratio vary across lines. Lines having a higher possibility or claim amount not being paid in full exhibit lower premium‐to‐expected‐loss ratio and higher equity‐to‐expected‐loss ratio. Positive correlation among lines of business results in lower premium‐to‐expected‐loss ratio than when independent losses are assumed. Positive correlation between investment return and losses reduces the insolvency risk and leads to a higher premium‐to‐expected‐loss ratio.