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Some of the assumptions underlying the Black-Scholes model. Do these limit its realism and predictive power?

A student asked

I want to ask why risk-averse has a decreasing marginal utility? Thank you.

Response:

If someone has a decreasing marginal utility of income and they maximise expected utility then they will be risk averse.

This is something that takes a long time to fully explain, and I try to give an explanation in the web-book and in lecture (and again in tomorrow's lecture).

One simple intuition.: Risk averse essentially means "I will never take any fair gamble".

E.g., "I'll never accept a bet with an equal chance of losing or gaining some amount X." How does diminishing MU of income explain this? If I have diminishing MU of income then my utility is increasing in income at a decreasing rate.

The first units of income (e.g., going from 0 income to 15k income) add more utility than the later units of income (e.g., going from 15k income to 30k income) , which adds more than even later increments (e.g., going from 30k to 45k), etc.

So "an equal chance of losing or gaining X" would not be attractive to such a person. Why not? Because relative to any point "losing X" reduces my utility more than "gaining X" increases it.

E.g., in the above example, if you started at 15K income you wouldn't want to have an equal chance of losing or gaining 15K in income. Having 0 income would be terrible, while having 30k income would be better, but not 'that much' better. As we said, the utility difference between 0 and 15K is much greater than the utility difference between 15k and 30k... because of the assumption of diminishing marginal utility. So it's better to have 15k for sure than to have a 50/50 chance of 0k or 30k.

The 'utility loss from losing 15k' is greater than the 'utility gain from gaining 15k'. As expected utility weights the utility of each outcome by its probability and sums these, in considering a 1/2 chance of losing 15k and a 1/2 chance of gaining 15k these probabilities weight equally, so I only need to consider "does the utility cost of losing 15k exceed the utility gain from gaining 15k" in this example. Because of diminishing MU, we know it does not. Nor does it for any "equal chance of losing or gaining some amount X". Thus this person is risk-averse.

I hope this helps. Looking at the 'utility of income' diagrams may also be helpful.

此 paper 回应并补充了去年何神的一篇说 pre-training 对 performance 鸟用不大的文章 (Rethinking ImageNet Pre-training)。你问是怎么回应的？瞅一眼此 paper 的题目就晓得了。。。。

It's nice to see that some things don't change :)

Cautionary note on making long-term forecasts with ecological models due to decreased accuracy with forecast horizon. This issue is made clear through the proper inclusion of uncertainty in the models.

Consigny quotes Bitzer's note that rhetorical situations may be "loosely structured" on the last page, and I'm interested in this quote as Consigny's response to that. How stable and determinate are these real issues? The criticism of Bitzer really seems to capitalize on the unknowable totality of a situation, so identify the situation is always incomplete. Do we bomb Iraq as a response to a fear of looking weak, a need for MIC profitability, or a sincere perception of danger? Even smaller cases, like with Bitzer's primitive rhetorics, the command to fulfill a task could always have ulterior motives the issuer isn't even wholly aware of.

I wonder how, in its use here, ambiguity is akin to curation. Noun v verb? Is v am?

The question that ambiguity evokes: what am I looking at? The question that uncertainty evokes: what do I do with what I am looking at?

Does the first question precede the second as we move through the world?

What Rao sez,

We live in a world with gradually increasing levels of uncertainty and ambiguity. Over the last few decades we've become much more comfortable with uncertainty, but still suck at dealing with ambiguity. Ambiguity is not knowing what you are looking at, as in those trick drawings that look like a rabbit one way, a duck another way. Uncertainty is not knowing what to do with what you're looking at. Unlike uncertainty, which is about missing or noisy information, ambiguity can exist even with complete, clean information. It is about interpretation and meaning, and is as such a truly creative act of seeing.

However, by usinglearningcomunitiesastheforuminwhichtheycan comparetheirownjourneysascriticalyreflectivelearners, adult educators realize that what they thought were idiosyncratic incremental fluctuations in energy and comitment,privatemoralesapingdefeatssuferedin isolation,andcontext-specificbarierspreventingchange, areoftenfeaturesthatareparaleledinthelivesof coleagues.Thisknowledge,evenifitfailstograntany insightsintohowthesefelingsorbarierscanbe ameliorated,canbethediferencebetwenresolvingtowork forpurposefulchangewhenevertheoportunityarises,and falingpreytoamixtureofstoicismandcynicisminwhich staying within comfortably defined boundaries of thought and action becomes the overwhelming concern.