This seems to assume that 100% of claims get approved. How can the equation be modified to account for the probability of claims being denied?
I would guess lower cost insurance policies tend to come from companies with lower claim approval rates, so it seems appropriate to price into the calculator. I believe there are also softer elements in insurance costs like this that should be considered, such as customer service quality, but that’s probably out of scope for this calculator.
Fundamentally we are taking the probability-weighted expectation of log-wealth under all possible outcomes from a single set of actions, and comparing this to all other sets of actions.
The way to work in uncompensated claims is to add another term for that outcome, with the probability that the claim is unpaid and the log of wealth corresponding to both paying that cost out of pocket and fighting the insurance company about it.
A refused claim is (legally) an event that was never covered by the insurance, and is therefore irrelevant if the question is “take policy A or not at all”.
After all, if that event occurred without insurance, it is still not covered.
However, this is important to consider when comparing different policies with different amounts of coverage. Eg “comprehensive” car insurance compared with “third party, fire, and theft”.
“Rates” of unpaid claims only make sense in a situation where the law allows the insurer to breach their contracts. In that situation, the value of insurance plummets, and possibly reaches zero.
This seems to assume that 100% of claims get approved. How can the equation be modified to account for the probability of claims being denied?
I would guess lower cost insurance policies tend to come from companies with lower claim approval rates, so it seems appropriate to price into the calculator. I believe there are also softer elements in insurance costs like this that should be considered, such as customer service quality, but that’s probably out of scope for this calculator.
Fundamentally we are taking the probability-weighted expectation of log-wealth under all possible outcomes from a single set of actions, and comparing this to all other sets of actions.
The way to work in uncompensated claims is to add another term for that outcome, with the probability that the claim is unpaid and the log of wealth corresponding to both paying that cost out of pocket and fighting the insurance company about it.
A refused claim is (legally) an event that was never covered by the insurance, and is therefore irrelevant if the question is “take policy A or not at all”.
After all, if that event occurred without insurance, it is still not covered.
However, this is important to consider when comparing different policies with different amounts of coverage. Eg “comprehensive” car insurance compared with “third party, fire, and theft”.
“Rates” of unpaid claims only make sense in a situation where the law allows the insurer to breach their contracts. In that situation, the value of insurance plummets, and possibly reaches zero.