Insurance risk and ruin by Dickson D.C.M.

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By Dickson D.C.M.

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Further, the investor would be indifferent between the two investments if E [u(W + X 1 )] = E [u(W + X 2 )] . 1 × 10 4 , 2000 2 ). Which of these investments does the investor prefer? 002). 002W } exp {−14} . Hence, the investor prefers Investment 1 as E [u(W + X 1 )] is greater than E [u(W + X 2 )]. Note that the expected utility criterion may lead to an outcome that is inconsistent with other criteria. This should not be surprising, as different criteria will, in general, lead to different decisions.

The remainder of the chapter is devoted to the important practical question of calculating an aggregate claims distribution. 5 we introduce certain classes of counting distribution for the number of claims from a risk. The importance of these classes is that if we assume that individual claims under the risk are modelled as discrete random variables, it is then possible to calculate the probability function for aggregate claims recursively. We conclude the chapter by describing two methods of approximating an aggregate claims distribution.

In practice, insurers have to take account not only of the characteristics of risks they are insuring, but other factors such as the premiums charged by their competitors. We denote by X the premium that an insurer charges to cover a risk X . When we refer to a risk X , what we mean is that claims from this risk are distributed as the random variable X . The premium X is some function of X , and a rule that assigns a numerical value to X is referred to as a premium calculation principle. Thus, a premium principle is of the form X = φ(X ) where φ is some function.

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