Optimal financial and ordering decisions of a firm with insurance contract

This paper examines the impact of a bank's risk limit on the financial and ordering decisions of a capital-constrained firm with insurance contract. All our major results can be computed via explicit expressions. It is shown that the bank will control its risk to be below the risk limit through setting a loan limit and the firm can make the loan limit increase by buying a deductible insurance policy. It is also shown that the repayment demand level needed to avoid bankruptcy will not be affected by the insurance policy. We derive the firm's optimal ordering quantity and insurance coverage level under a downside risk measurement and a variance risk measurement separately. It is shown that the firm should pay more attention to whether to buy insurance or not under the downside risk measurement and how much insurance coverage to buy under the variance risk measurement. Under the downside risk measurement, once the firm decides to buy insurance, the optimal coverage level is independent of the bank's risk limit. We also show that the insurance contract has a more obvious effect on the profit increases when the selling price is high or the bank's risk limit is low.