| Abstract: | We introduce costly internal capital into a standard insurance model, in which a risk‐averse policyholder buys insurance from a risk‐neutral insurer with limited liability. The unique optimal contract and internal capital lead to a strictly positive probability for insurer default. Some risks are uninsurable in that the insurer chooses not to provide insurance against such risks. An increase in the cost of capital may lead to a higher optimal amount of internal capital. The results extend to multiple policyholders in a symmetric setting. Our extension of the classical model to include costly internal capital provides a fruitful approach to many real world insurance markets. |
