Mathematical Model and Management of Premium Fund in Takaful Insurance for Hybrid Scheme

Takaful is a type of insurance in which participants contribute a certain amount of money to a common pool in an exchange for protection against predefined losses. The hybrid model (wakalah-mudharabah) is one of business models which can be used by Takaful Operator to manage the Takaful fund in a compensation of wakalah's fees which paid upfront and a profit-sharing from investment activities for its services. This paper will discuss about the mathematical model with respects to the management of premium fund in takaful insurance under the hybrid scheme. We took samples for participants aged 25, 45, and 65 years from the 2019 Indonesian mortality table in the calculations. We noted that the probability of death for male is relatively higher in comparison with the female. Subsequently, we compared the behaviour of total takaful operator's profit based on several indicators, such as participant's gender, participant's age, and the amount of benefit. Based on the participants' gender, the total profit earned by takaful operator from male group was slightly higher than for those in female group, but during the last year of policy years, it indicated the opposite figure. The second comparison was based on the participants' age. We observed that the older age provided more profit to the operator than the participants with younger age. However, as the policy years increased, it indicated the opposite figure. Finally, the difference in the amount of death benefit received by the insured had a constant effect on the total profit for takaful operator.