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in BUS 4027W - Actuarial Risk Management by

How can two risks be matching and yet negatively correlated or even uncorrelated?

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by (460 points)
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For the section you are referring to in the notes (5.5 in Chapter 44). The 'matching' is reffering to different organistations with similar risk exposures.  

Thus, as in the example below it, one organisation exposed to say catastrophe risks in one geographical area can swap some of these risks with another organisation in another geographical area. These are the same type of risks (thus matching) however the difference in geographical areas will allow diversification of the risks, as they are at least uncorrelated. 

by (460 points)

So the risks are matching, as in they are the same type of risks, but the negative correlated or uncorrelated feature of the risks is due to the specific circumstances of the different businesses. 

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Think of longevity risk and mortality risk.

These are clearly negatively correlated.  If we were extremely prone to longevity risk, we could swap a book of life annuities for an equally valued book of whole-life assurances.  This will decrease our longevity risk and increase our mortality risk.  Therefore if there is an adverse mortality experience, the losses we make from the higher number of death benefits paid out will be somewhat canceled by the decrease in the number of annuity payments we will have to pay.  Similarly, they will be somewhat canceled if mortality experience is light.