Since banks lend out at long maturity, they cannot quickly call in their loans. And even if they tried to call in their loans, borrowers would be unable to pay back quickly, since their loans were, by assumption, used to finance long-term investments. Therefore, if all depositors attempt to withdraw their funds simultaneously, a bank will run out of money long before it is able to pay all the depositors. The bank will be able to pay the first depositors who demand their money back, but if all others attempt to withdraw too, the bank will go bankrupt and the last depositors will be left with nothing.
In this case the system works fine if interest changes are asynchronous and adjustable, and the traders are risk adjusted which is equivalent to closure. This is the stable model.
Then treat term loans as an insurance business. Thus instability in the insurance business is separated in the analysis. Insurance companies insure time between disasters.
This discussion cam up on the boards, and yes, adaptive fractional reserve banking works, in its raw form. But the fraction should seldom be less than 90%. If the fraction is less then it is likely a rare event treated as over the counter trade needing insurance.
This is simple stuff, folks, obvious dimensional analysis, clearly using Markov to judge market size for adequate liquidity. Our price variation is about 4%, if someone can beat that to 7% and up, then that trader should be OTC, it is not a batch S/L fractional asynchronous service.
Sandbox is well layered and we cracked this problem years ago.
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