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Über dieses Buch

The Fundamental Issues Involved Why do we need a theory of uncertainty? It is a fact that almost all man's economic decisions are made under conditions of uncertainty, but this fact alone does not provide a strong enough argument for making the effort necessary to generalize ordinary preference theory designed for a world of perfect certainty. In accordance with Occam's Razor, the mathematician may well welcome a generalization of assumptions even if it does not promise more than a restatement of known results. The economist, however, will only be well disposed towards making the effort if he can expect to achieve new insights and interesting results, for he is interested in the techniques necessary for the generalization only as means to an end, not as ends in themselves. A stronger reason for developing a theory of uncertainty, therefore, seems to be the fact that there are kinds of economic activities to which the non-stochastic preference theory has no access or has access only through highly artificial constructions. Such activities include portfolio decisions of wealth holders, speculation, and insurance. These will be considered in detail in the last chapter of the book. The main purpose of this book, however, is not to apply a theory of uncertainty to concrete economic problems, the purpose rather is to formulate such a theory.

Inhaltsverzeichnis

Frontmatter

Chapter One. The Object of Choice under Uncertainty

Abstract
It is the task of preference theory to indicate general criteria by which men choose, or should choose given their preferences, from a set of mutually exclusive action alternatives (a1,a2,...,a m ).
Hans-Werner Sinn

Chapter Two. Rational Behavior under Risk

Abstract
In chapter one, general decision problems under uncertainty were reduced to the case of pure risk. The next question is how the economic decision maker will evaluate objective risks, that is, what are the properties of the preference functional R(.) in the case of objective probabilities. This chapter attempts to give a partial answer which determines some basic rules for rational behavior under risk. The following chapter is devoted to the task of formulating a supplementary hypothesis concerning man’s preferences.
Hans-Werner Sinn

Chapter Three. The Structure of Risk Preference

Abstract
In the two preceding chapters it was shown how consistent decisions can be reached under uncertainty. By the use of, subjectively formed, equivalent objective probabilities the expected utility of each decision alternative has to be determined and then the alternative with the highest level of expected utility must be chosen. Unfortunately this advice remains quite meaningless as long as all that is known is that the utility function reflects the decision maker’s preferences, while the form of this function is quite unknown. This chapter, therefore, attempts to gain more specific information on the shape of the utility function.
Hans-Werner Sinn

Chapter Four. Multiple Risks

Abstract
Up to now, the analysis has been limited to a single period of time where a single risk project has to be chosen. This chapter provides a twofold generalization. On the one hand we discuss the possibility that the risk projects referred to previously come about by summing up the incomes of various non-rival subprojects that can be carried out at the same time. On the other hand, as promised earlier, we proceed to the analysis of repeated choice under risk. If, in the second case, the optimal sequence of risk projects had to be determined before the sequence starts1, then, except for the interest problem, it would not differ from the first. However if we assume realistically that, at the beginning of each period, the decision maker again may choose between the risk projects of that period knowing the outcomes of all previous decisions, then there is a decision problem of a new kind which requires a separate analysis. Moreover, in the multiperiod case, it seems that we can no longer factor out the problem of a simultaneous optimization of the consumption decision which was briefly considered in chapter one.
Hans-Werner Sinn

Chapter Five. Areas of Application

Abstract
The theory of decision making under uncertainty developed above has a large number of possible applications. Here we consider in more detail three of them only: optimal portfolio management, currency speculation, and insurance demand. These areas of interest seem to be good examples of problems that are difficult to handle with nonstochastic theories.
Hans-Werner Sinn

Backmatter

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