# First Course in Integration by Edgar Asplund, Lutz Bungart

By Edgar Asplund, Lutz Bungart

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Example text

2) Establish/predict the choice pattern of the second lottery-pair by means of the first ranking and the rules of EUA, namely employing its independence- and compound assumption. (3) Interpret contradictions between the observed and the predicted choice pattern of the second lottery-pair. Before coming to the interpretation let me firstly present the three rather well-known choice patterns and secondly contrast them to the 'implications' of EUA. 22 The following examples are taken from D. [ 1979].

Bressler [1975, pp. 329334] ) 49 sign of {d[dW/dPldU(L)=O]/dp} is given by: sign{ dp } dU=O sign {[U(w+g)-U(w)][U' (w+g)-U' (w)]} Assuming concavity [U'(w+g) < U'(w)] the sign will be negative, indicating that the marginal option prices, the absolute value of [dw/dPldU(L)=O]), will actually increase with p for agents with an exponential von Neumann/Morgenstern utility function over money! This pattern, however, was considered paradoxical by J. Drukarczyk [1978]. Yet, this vindicative finding is only of little use when it comes to retaining/rejecting EUA for the purposes of real physical risk analysis as the above line of argument only refers to 'clinical' findings from the realm of money.

C. J. 673] on this point, notably on the need of real-world field studies before transferring 'clinical' results. 2. From Financial- to Physical certainty Effects Let us begin with a famous example from the twilight-zone of 'semi-reality', the so-called Zeckhauser paradox. "There are six chambers in a revolver and k of these chambers -- in the usual version k = 1 -- are loaded; the rotating drum is spun in a way that each chamber has an equal chance of being used. Hence the [player)31 has a k/6 chance of meeting his demise.