Use of put options as insurance

An important question in insurance is the amount of coverage to purchase. A standard microeconomic model for insurance shows that full insurance is optimal. I present a different model where the decision variable is the number of put options and show that full insurance is still optimal, but the number of put options required to achieve this is larger than the endowment of risky assets. The model I present is based on a binomial model for a financial market, where the put option represents insurance.