As you age, you should be converting your earnings to financial assets. You likely own larger homes and have investment portfolios that you want to protect against disasters and lawsuits. If your home burns down, or if you injure or kill someone in an automobile accident, a lifetime of wealth accumulation could easily be wiped out. Therefore having the right insurance can help to protect valuable assets.
Fortunately, the likelihood is low that catastrophic events will occur, so the cost of insuring for them is normally reasonable. Protecting assets from lawsuits is also critical, so consider getting a low-cost umbrella policy. How much umbrella liability coverage is needed is definitely a judgment call. A general rule of thumb is to have an umbrella liability policy equal to your net worth, but even that is debatable since you can always be sued for more than your net worth.
The principle of self-insuring is still important. Higher deductibles are a form of partial self-insurance. If you can save $500 annually by raising the deductible by $1,000, then the maximum loss you would incur is $500 - the $1,000 higher deductible less the $500 savings; and by the third year without a claim you have already come out ahead. In addition, if you have a low deductible, it may not pay to make a claim when the payout would be small and reporting the loss would increase future premiums.
The principle of self-insuring is still important. Higher deductibles are a form of partial self-insurance. If you can save $500 annually by raising the deductible by $1,000, then the maximum loss you would incur is $500 - the $1,000 higher deductible less the $500 savings; and by the third year without a claim you have already come out ahead. In addition, if you have a low deductible, it may not pay to make a claim when the payout would be small and reporting the loss would increase future premiums.