Yes. There is extensive literature on bank runs and similar failures caused by fractional or fraudulent reserves and lack of confidence, insurance, and regulation.
Can you please go into more detail on these "interesting properties"? I fail to see anything in terms of real analysis in the links you gave, simply descriptions of automated trading rules simple enough to be understood, but mathy enough to sell to the marks if cryptocurrencies, backtested on the growth stage of a bubble.
It solves the problem of decentralised liquidity. An order book with traditional market makers is inherently centralised, here we have incredibly simple algorithms for trading between two assets with no intermediary, and the complicated, HFT market makers of traditional finance are replaced by passive liquidity providers.
Not sure why you mention backtesting, or how that would really apply.
So basically, there is no interesting inherent property (no interesting math, no deeper dynamics), it just "solves" a problem DeFi created - and it only introduces a whole new layer of possible implementation errors and new types of risks like impermanent losses.
Backtesting is relevant because there was no stability analysis, no simulated long drawn out bearmarket, no adversarial probing. Just some minimal quant sugar to make the new gambling opportunity go down with the suckers.
In real finance, you have much more sophisticated and diversified trading algorithms babysitted and regulated for stability, with much higher effective decentralisation and control since different HFT funds are legally barred from conspiring against the traders. Oh, and much lower fees as well.
I'm completely bewildered at what you mean in this context, given that the most conservative possible viewpoint on stablecoins is "there is no algorithm that can produce a stable coin other than 100% or better reserves in the stated currency".
Remember that "conservative" in finance means not taking risks, rather than the current political meaning of "right wing authoritarian".
I'd read up on the Uniswap constant product invariant (xy=k) and consider reading the Uniswap v2 code (it's a pleasure to read) [0].
Then check out the StableSwap paper by Curve founder Michael Egorov [1]
Finally if you want a well-documented implementation to read in Solidity, check out Saddle [2]. Disclaimer, I helped write the first iteration.
[0] https://github.com/Uniswap/v2-core [1] https://curve.fi/files/stableswap-paper.pdf [2] https://github.com/saddle-finance/saddle-contract/blob/maste...