Make sense. I suppose we assume that the insurance pays out the value of the asset, leaving our wealth unchanged. So assuming we buy the insurance, there’s no randomness in our log wealth, which is guaranteed to be log(W-P). The difference between that, and our expected log wealth if we don’t buy the insurance, is V. That’s why log(W-P) is positive in the formula for V, and all the terms weighted by probabilities are negative.
Make sense. I suppose we assume that the insurance pays out the value of the asset, leaving our wealth unchanged. So assuming we buy the insurance, there’s no randomness in our log wealth, which is guaranteed to be log(W-P). The difference between that, and our expected log wealth if we don’t buy the insurance, is V. That’s why log(W-P) is positive in the formula for V, and all the terms weighted by probabilities are negative.