Optimal Insurance Under Equity Risk Premium And Regulatory Requirements

Insurance transfers risk from the insured to the insurer.During this process,a contract needs to be reached to stipulate the amount of indemnity and premium.The insured expects to maximize his utility while the insurer should satisfy requirements from supervisors and his shareholders.At present,supervisors have paid more and more attention to solvency of the insurer.If requirements of solvency are not satisfied,the insurer will be restricted when developing new products and carrying out business which makes solvency so important to the insurer.Meanwhile,as investors of company,shareholders expect to get profit from dividend or stock market,otherwise they won't continue to invest in the insurer.In this paper,firstly,we design the optimal insurance under the constraint of solvency.Secondly,we add the requirement of shareholders as a new constraint and study the optimal insurance under the constraints of shareholders'equity and solvency.Thirdly,we give some examples based on our model and show the economic implications of the theoretical results.Different from the previous literature,in this paper,we focus on property insurance and design the optimal insurance under the constraints of shareholders',equity and solvency.We also study the characteristics of the optimal insurance.We believe our study extend the previous literature.Adding these new elements into the optimization problem leads to the following conclusion.Firstly,if we only take solvency requirement into consideration,optimal insurance involves one deductible when insurer is free of constraints.When solvency constraint is binding to the insurer,optimal insurance is 3-segment piecewise linear function and the reimbursement of the middle segment is fixed.Secondly,if we consider both solvency requirement and equity risk as constraints simultaneously,optimal insurance involves one deductible when insurer is free of constraints.When one of the constraints is binding to the insurer,optimal insurance is 3-segment piecewise linear function and the reimbursement of the middle segment is fixed.When both of the constraints are binding to the insurer,optimal insurance is a 5-segment piecewise linear function and the reimbursement of the second and fourth segment is fixed.Based on our conclusions,we think the insurer can improve their ability of risk management by setting different deductibles towards different loss which will be helpful in traffic compulsory insurance market and catastrophe risk market.