In an insurance company, it is very possible that there is an imbalance between the amount of the premium and the amount of claims submitted by the insured. In managing the risk of such an imbalance, the insurance company must be able to make a decision to determine the appropriate amount of premium based on a number of claims by the insured. To make these decisions, insurance companies can do so by using certain utility functions. This paper examines the use of exponential utility functions in transferring risk between insurance companies, optimal Pareto exchanges, equilibrium, Bowley solutions, and optimal reinsurance purchases. Furthermore, using the exponential utility function is calculated the optimal amount of reimbursement that will be carried out by the insurer. The results of the discussion obtained the factors that influence the calculation and the optimal amount of reimbursement value, from a property policy or group policy that needs to be carried out by the insurer. So that based on the results of the optimal reimbursement calculation, it can be used to determine the balance between the amount of the premium and the amount of claims that may be submitted by the insured.
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