Channelling global private investments to energy efficiency in buildings

Buildings account for more than 30% of global final energy consumption, and are thus some of the largest consumers of energy in the world. With future demographic increases forecast, this figure is set to rise. Currently, the main focus of building policies is often on new buildings. However, the potential lies, at least in the Northern hemisphere, in existing buildings. And this sector is in dire need of fresh money for investments in renovation.
In a parallel set of events, there is growing discussion in international public banks, such as the European Investment Bank, on the need to help large-scale investors and pension funds diversify their portfolios. Insurance companies are in fact hit in two ways by climate change, firstly by more significant damages to insured properties and secondly by the loss of profitable dividends such as investments in the oil sector.
Linking these two processes, what can be done to redirect global private investments to the building sector?