Economic Foundations for Finance by Thorsten Hens & Sabine Elmiger

Author:Thorsten Hens & Sabine Elmiger
Language: eng
Format: epub
ISBN: 9783030054274
Publisher: Springer International Publishing

This property is called Jensen’s inequality in mathematics and is illustrated in Fig. 6.2. The left plot assumes that all values of C, i.e., C 1, …, C Z, lie within the interval , and the expected value lies somewhere in this interval. The values and follow directly from the graph of the utility function. To determine expected utility

we draw an auxiliary line between the two points and . According to the theorem of intersecting lines (see Sect. A.14), the expectation divides the interval into the same proportion as the point divides the auxiliary line. We see that due to the curvature of the utility function, holds.

Fig. 6.2Concavity and risk aversion. The left plot illustrates the shape of the utility function and the connection to risk aversion. The right plot shows the special case of two states that occur with equal probability

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