#### Date of Award

Spring 1985

#### Project Type

Dissertation

#### Program or Major

Engineering

#### Degree Name

Doctor of Philosophy

#### Abstract

The conventional theory of decision making under risk relies on axioms that reflect assumptions about people's subjective attitudes towards wealth. The assumptions are unverifiable, and the axioms are too restrictive. They forbid some decision rules that a plausibly rational decision maker ("DM") could find useful.

A new method, at once less restrictive and less dependent upon subjective assumptions, motivates expected utility techniques by assuming that a DM wishes to place an upper limit on the probability of ruin. All bounded-above, increasing functions defined over a suitable domain can serve as utility functions.

Now, DM can evaluate lotteries according to their buying prices, useful if one plans to withdraw capital from risk. DM can rigorously distinguish "once in a lifetime" lotteries from ordinary gambles; that's helpful when facing Allais' problem. Also, DM can exploit partial knowledge of state probabilities without choosing arbitrary point estimates for all uncertain odds. That helps to resolve problems that combine elements of both risk and uncertainty, like Ellsberg's.

The new method allows DM to do everything permitted under the old axioms, and more besides, with fewer and less ambitious assumptions.

#### Recommended Citation

SNOW, PAUL, "RISK AND UNCERTAINTY (UTILITY, DECISION)" (1985). *Doctoral Dissertations*. 1455.

https://scholars.unh.edu/dissertation/1455