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Maximum Sustainable Benefits to Avoid Operating Losses

Insurers' Maximum Sustainable Benefit For Avoiding Losses, $MSBAL_N$, are the highest portions of premium dollars they can provide, as benefits, throughout the year, while matching $PI$'s probability (0.9772) of avoiding operating losses. To adjust for their differences in PLRE variability, $MSBAL_{NHI}$ = 0.8500 - 2 * $\sigma_{e_{N}}$ because PLREs above 0.8500 produce operating losses. Table 1 Row 13, shows that $MSBAL_{NHI}$ = 0.8443; $MSBAL_{B}$ = 0.8184; and $MSBAL_{PI}$ = 0.7500. $MSBAL_{D}$ = 0.5338 and because $\sigma_{e_{E}}$ is ten times larger than $\sigma_{e_{PI}}$, $MSBAL_{E}$ is less than 0.0000 (0.8500 - 2 * 0.5000), because $E$'s probability of losses (0.4207) is much higher than PI's (0.0228).

Insurers' Maximum Average Benefits Per Policyholder To Avoid Operating Losses $MABPPL_N$ are the highest benefits, in dollars, ($MABPPL_{N}$ = $MSBAL_{N}$ * $4,000) insurers can pay, while matching $PI$'s probability (0.9772) of avoiding operating losses. Table 1 Row 14, lists these benefits. $MABPPL_{NHI}$ = $3,377, $MABPPL_{B}$ = $3,274 and $MABPPL_{PI}$ = $3,000. $MABPPL_{D}$ = $2,135 and $MABPPL_{E}$ $<$ $0.00.

Matching $PI$'s ability to earn profits is easier than matching $PI$'s ability to avoid losses, because the more loss smaller insurers are, the more they need to cut benefits, to match $PI$'s probability of avoiding losses. $PI$', $D$'s and $E$'s probabilities of earning profits, or incurring losses, are similar near the PLR, but rapidly diverge above the PLR, making it increasingly more difficult to match $PI$'s performance.


next up previous contents
Next: Risk Adjusted Premiums Up: Insurer Risk and Maximum Previous: Maximum Sustainable Benefits for   Contents
Thomas Cox PhD RN 2013-02-23