# Q&A about Problem Set 5 with Fin4335 Student

Email from Fin4335 Student:

I just had a question about the problem set if you have the time. For part e, how are we supposed to know what the premium loading factor is? Because in the spreadsheet example that was used in the calculations but i don’t see how you are supposed to find that number in the problem set.

Email from Dr. Garven back to Fin4335 Student:

The price of insurance (AKA the “insurance premium”) is $P = E(I)(1 + \lambda )$, where $E(I)$ corresponds to the expected value of the indemnity, and $\lambda$ corresponds to the premium loading factor. When $\lambda$ = 0, then $P = E(I)$; i.e., insurance is actuarially fair.  As I pointed out during class last Thursday, $\lambda$ > 0 in most private insurance market settings; i.e., insurance is typically actuarially unfair because firms incur transaction costs in forming and managing risk pools.  It follows (from the insurance pricing equation given above) that $\lambda = P/E(I) - 1$; i.e., the premium loading factor represents the percentage markup over and above the actuarially fair premium.

The first step in solving Part E (as noted in today’s Problem Set 5 Helpful Hint) requires determining the state-contingent indemnity schedules ( ${I_s}$) for the four risk management strategies (i.e., self-insurance, full insurance, deductible insurance, and coinsurance).  These indemnity schedules represent the contractually agreed upon payments made by the insurer to the consumer under each contract in each of the three loss states.  Once you’ve figured out the state-contingent indemnities for each policy type, then calculate the expected values for each indemnity schedule (i.e., $E(I) = \sum\limits_{s = 1}^3 {{p_s}{I_s}}$). Since the insurance prices (premiums) are $3,125 for Policy A and$2,500 for both Policy B and Policy C, then finding the premium loading factor for each policy is straightforward.