Optimal brokerage commissions for fair insurance : a first order approach

This paper studies a principal-agent insurance brokerage problem with a risk-averse principal (an insured) and a risk-neutral agent (a broker). The concept of mean-preserving, spread-reducing (MPSR) effort is introduced to model the broker's activities. Using the first-order approach, it is shown that under some common conditions, the insured may concavify the reward function to induce the risk-neutral agent to exert MPSR brokering effort. These conditions, together with an additional condition, guarantee the validity of the first-order approach even when the monotone likelihood ratio condition (used exclusively to justify the first-order approach) is violated.