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I am new to decision theory and currently I am reading the book 'Making Better Decisions: Decision Theory in Practice' by Itzhak Gilboa. I am fascinated by the discussion of utility function and risk aversion. After reading the corresponding chapters, the following problem is imposed:

It is often argued that the value function in Kahneman and Tversky's prospect theory is convex in the domain of losses, that is, individuals behave in a risk loving way when it comes to losses. How can this be reconciled with the fact that people buy insurance (where premiums exceed expected losses)?

I think I did not completely 'digest' the ideas introduced in the book. I understand that there is gain-and-loss asymmetry and therefore people tend to averse losses. For the question above, since people do not want to suffer from accident, they are willing to pay more so as to prevent such loss. Am I right? But if I pay the premium, isn't it already a loss to me? I hope that some of you can explain this to me briefly.

Thanks in advance.

Maybe I quote what the book says about the loss aversion:

...The decision maker has a certain reference point with with payoffs are compared... This loss aversion goes beyond the obvious fact that people prefer more money to less. It suggests that a given amount of money, if perceived as a loss relative to the reference point, will be considered a more painful outcome than the same amount when perceived as a gain.. Importantly, prospect theory holds that people react to changes rather than absolute levels.

Nighty
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  • Can you quickly clarify for us the claims of the prospect theory? – Travelling Salesman Feb 20 '15 at 13:35
  • @Travelling Salesman : One important point is that people 'treat gains and losses differently'. In particular, people avoid losses. – Nighty Feb 20 '15 at 13:42
  • Thanks @LeeKM, I'm aware there's an asymmetry - with experiments showing people are more loss-averse than they are gain-positive.

    It's more I was puzzled about you saying K and T's prospect theory is risk-positive with losses. Can you explain that a bit more? What do they mean?

     – Travelling Salesman Feb 21 '15 at 19:03
  • @TravellingSalesman : See the edit above, thanks. – Nighty Feb 22 '15 at 07:16
  • That sounds more believable, I agree @LeeKM. I suppose an insurance premium paid to forestall a loss is itself a kind of loss, but most decision theorists would probably treat it as a measure of how much more risk-averse most people are than gain-positive. If risk-averseness matched gain-positivity evenly then people would be averse enough to the 100% likelihood times small premium as they are averse to the smaller % likelihood of bigger bad outcome to not buy the insurance policy, right? Insurance policies aren't lottery tickets with high gain multipliers. – Travelling Salesman Feb 22 '15 at 11:16

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