How do we calculate a reserve if we have two triangles - one of paid claims and one of incurred claims?
In exam questions - you only have one or the other. In real life my understanding is that incurred is used as it is less "lumpy" than claims paid.
Actually, if you go on to study ST7, you'll find that both are used in real life! Incurred is indeed less lumpy and uses more information (not a bad thing!) - but if case estimates are unreliable then paid may be better, particularly if paids are very predictable. If the business is short tailed (like household, for example), then it may make little odds which one you use. In practice, of course, given the ease of using spreadsheets, why not use both and look at the difference - maybe even take the average of the two! Then of course there are a host of other methods that are used in practice. But I'll keep those a secret to try and get your interest for ST7!
