However, "Pareto optimality" can be far from a "solution beneficial for everyone" in your OP.

For example, Elon Musk can consume all the output and that can be Pareto optimal, as taking output from him and allocating it to others may lower his utility. However, Pareto optimality seems a useful notion when there are wasted resources, barriers to competition, unnecessary regulations, etc.

I am not an economist, so I'm sure this is only part of a good answer.

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It might be a bunch of basic stuff for you, but maybe some of the below might help:

- Economics: Arrow's Impossibility Theorem and this interesting paper https://ieeexplore.ieee.org/document/84 ... rs#authors

- Applied Ecology: good models survey https://www.nature.com/articles/s41559-020-01298-8#Bib1

- Complexity Theory: Porf Farmer's landing page http://www.doynefarmer.com/presentations

Rgds,

M

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Statistics: Posted by katastrofa — Today, 2:24 pm

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Statistics: Posted by Amin — Today, 8:29 am

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Where is Monty Python when you need them? Although, maybe we don’t need them. He is doing a perfectly splendid job of mocking himself.

You say that like it’s a bad thing!Statistics: Posted by Paul — Today, 7:44 am

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Is AI now a bigger scam than Finance?

Always was. The AI madness returns regularly like waves, the first one I know only from the literature was in the 50-ties.Statistics: Posted by Gamal — Today, 6:51 am

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Statistics: Posted by Marsden — Today, 12:30 am

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Statistics: Posted by katastrofa — Yesterday, 10:53 pm

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Statistics: Posted by tagoma — Yesterday, 9:16 pm

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To frame an option pricing model requiring (or, more practically, worked in reverse, implying) a risky discount rate requires imposing some restrictions on utility preferences (as per Rubinstein, Ross, and Carr) or an asset pricing model (e.g. CAPM, APT). I took the latter approach in the late 1980’s, as I was suspicious of aggregating utility from the small to the large.If memory serves me right, he was applying a pretty standard discounted expected cash flow argument to Samuelson’s lognormal stock price model to find the present value of the option. That gives you the right general shape of the resulting valuation formula, but with a risk adjusted discount rate that is hard to determine.

An interesting practical problem is that a formulation with risky discount rates introduces a second unobservable into the valuation equation, which complicates things. Joint estimation of implied volatility and expected return from the same data is possible but messy. I used a 2-step procedure – first imply Black-world vols, and then use that vol in the risky discount rate option model to back out expected return from option price.

A related question if you would humour me – within the assumptions of the model, is the usual risk-neutral Black Scholes implied volatility an unbiased estimate of real world vol, or is somehow affected by the risk-neutral valuation? I vote for the former.

Statistics: Posted by Alan — Yesterday, 7:12 pm

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