No, the risk is the probability of a claim times the value of a claim. If you just charge that is mathematically proven that the insurance pool is going to fail. The actuarial adjustment is there to create a surplus that guarantee the survival of the pool.
The return of capital is what the owners of the capital expect to get to have their money invested on the insurance company instead of moving their money to other investment opportunities.
But the capital provided by the owners is what is used to backstop the insurance and ensure the pot always exists. The amount of capital needed is calculated by the actuaries but supplied by the owners.
This is why I’m confused why you listed both an interest on capital and an actuarial adjustment.
Aren’t the risk and the actuarial adjustment the same thing?
No, the risk is the probability of a claim times the value of a claim. If you just charge that is mathematically proven that the insurance pool is going to fail. The actuarial adjustment is there to create a surplus that guarantee the survival of the pool.
Yes, you need to hold enough money to cover more/larger claims than expected, but doesn’t the return on capital cover that part?
The return of capital is what the owners of the capital expect to get to have their money invested on the insurance company instead of moving their money to other investment opportunities.
But the capital provided by the owners is what is used to backstop the insurance and ensure the pot always exists. The amount of capital needed is calculated by the actuaries but supplied by the owners.
This is why I’m confused why you listed both an interest on capital and an actuarial adjustment.