Engineering Risk and Finance pp 333-374 | Cite as

# Uncertainty Economics

## Abstract

This chapter seeks to reconcile fundamental financial approaches with uncertainty. Uncertainty is defined by the unknown rather than the predictable, counted and accounted for. While financial decisions are reached based on what we know, what we can predict and what we can presume based on experience and the rationalities that financial agents assume. The uncertainty we consider is defined in a limited sense, namely, a partial knowledge of future state preferences and their quantification. There are many approaches to do so such as negligence of the unknown, human intentional rationalities as well behavioral and psychological approaches to confront the unknown. This chapter focuses its attention on the use of entropy for “non-extensive systems” (a term commonly used in physics with its parallel in finance, which we define as “incompleteness”) based on a parametric generalization of the Boltzmann–Gibbs entropy (which assumes extensive systems). Optimization of the Tsallis parametric entropy for non-extensive systems is then used to derive implied power laws and standardized probability distributions that are both asymmetric and have fat tails. This approach provides a parametric definition of the “missing”, namely the tail probabilities not accounted for in selecting an asset future price distribution.

Subsequently, the chapter outlines a number of approaches to robust decision models and ex-post risk management. It concludes with a discussion of risk externalities in financial and environmental regulation and draws a parallel between “banks’ risks” for which they do not assume responsibility for and pollution risks of firms and consumers who consume and who do not assume their pollution consequences. Both cases, call for an efficient regulation and statistical controls which is the topic of Chap. 11.

## Keywords

Risk Model Generalize Entropy Prospect Theory Positive Externality Insurance Contract## References

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