By Fabrice Collard, Frédéric Boissay, Jordi Galì and Cristina Manea
http://d.repec.org/n?u=RePEc:tse:wpaper:126275&r=dge
We study whether a central bank should deviate from its objective of price stability to promote financial stability. We tackle this question within a textbook New Keynesian model augmented with capital accumulation and microfounded endogenous financial crises. We compare several interest rate rules, under which the central bank responds more or less forcefully to inflation and aggregate output. Our main findings are threefold. First, monetary policy affects the probability of a crisis both in the short run (through aggregate demand) and in the medium run (through savings and capital accumulation). Second, a central bank can both reduce the probability of a crisis and increase welfare by departing from strict inflation targeting and responding systematically to fluctuations in output. Third, financial crises may occur after a long period of unexpectedly loose monetary policy as the central bank abruptly reverses course.
That central banks should deviate for their inflation mandate is not objective, after all for most them a law or some sort of contract with the government restricts them to just that. Yet it is generally understood that they also should care about output and/or employment. And as history has shown, financial crises do have an impact on output and employment. Thus it seems natural that central banks should keep an eye for financial trouble. The paper argues that this best done by preventing over-investing and then reacting to that late and abruptly. This year is going to be interesting.
NEP-DGE Blog 
In her 8 December speech (see https://www.ecb.europa.eu/press/key/date/2021/html/ecb.sp211208_2~97c82f5cfb.en.html), ECB board member Isabel Schnabel concluded that “taking financial stability considerations into account does not mean that financial stability is itself an objective of monetary policy. But there is a broad consensus that it is a precondition for achieving price stability.”
In its recent monetary policy strategy review (see an overview here https://www.ecb.europa.eu/home/search/review/html/ecb.strategyreview_monpol_strategy_overview.en.html), the ECB explicitly recognised this interdependence between price and financial stability. It decided to beef up its monetary analysis pillar by systematically evaluating the longer-term build-up of financial vulnerabilities and imbalances and their possible implications for future tail risks to output and inflation. This is in line with the findings and prescription of the paper.
Preventing over investing would require more accurate pricing on loaned capital, more over stopping that late/abruptly would simply mean that capital would have to be reappropriated in accordance with changes in “capital prices” or liquidity which all but the text book definition of a correction.
And by a cursory look thats your argument for preventing one?