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Any thoughts?

I am most definitely a mathematical light-weight, but I am also fascinated by the concept of risk analysis.

When Buffett decided $11 was too great a price to pay for a $10,000 return he was evaluating his own ability at golf. He may have taken another look if Tiger Woods was the one at the tee.

So, perhaps the 'human input' aspect of the equation you are looking for is what makes it most difficult to evaluate risk. Buffett was also expected to risk his entire $11, win or lose, with no opportunity to recover a portion. If it had in fact been $11 million that he was investing, he would have done so with an expectation that a poor result would leave only a dent in his capital. I think the risk of total loss through wagering was what turned Buffett away from his early interest in horse-racing, as it is very difficult to protect capital and therefore stay in the game when any and possibly every wager may represent a total loss of the money-at-risk.

Professionals who bet on the outcome of races use their experience and knowledge to give each runner a value. If their best-value runner is offering an overlay, a higher return than they have essed it to be worth, then they bet a small portion of their total working capital against the market. If the market has taken to their selection and driven the offering down, then they walk away without taking a risk. If it were any easier than that the market would not exist, and if the essment of risk in insurance were any easier that market would falter also.

Your equation would need total capital times percentage at risk on one side and the probability of success or failure on the other, and the strange and unexpected things that people do make the essment of probability mind-boggling. The accuracy with which an insurer can manipulate such an equation will determine whether or not they attract business and remain liquid, both at the same time.
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