In applying typical EU models, we need to assume 1) some utility function, and 2) the PDF of wealth, including how wealth is affected by alternative outcomes. However, U(W) is rarely known, and risk aversion coefficients may be controversial. Eliciting U(W) and ra/rr are, in many cases, unreliable. Elicitation of joint PDFs is likewise complicated.

There are preferable alternative methods to analyzing decisions under risk when historical data on yields, prices, costs, and returns associated with different technologies or products is available. The usual caveats apply for historical data, for example, are they i.i.d? In addition, how accurately do historical data series represent the subjective probabilities of the DM?

Typically, the observed (historical) probabilities are equated with the subjective probabilities of DM, assuming that the data generating process of historical data is connected in some way to profit or utility-maximizing (or cost minimizing) behavior.
It is impossible to advance in research without making assumptions. Hopefully, the assumptions we do make are not objectionable but are still affective for assisting the expected utility maximizing decision process under study.

[This note was edited by the lecturer and is the most updated one, if you see any errors or omissions, please advise...]