Individual with wealth level w0 and VNM utility function u must decide
whether and how much to insure his car. There is probability 0<a<1 of
accident in amount of L dollars. Insurance is available at an actuarily fair
price (each dollar of insurance costs p=a). How much insurance will
individual buy?

Risk averse individual (concave VNM) will buy x=L dollars of insurance. That
is clear. Risk neutral individual (linear VNM) will buy 0<x<L of insurance.
But why will risk loving individual (convex VNM) buy x=0 dollars of
insurance? I would need an analytical solution.

Thanks.

V.M.

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