The headline of the BBC report notes that the IEA projects greenhouse gas concentrations increasing 52%, as world energy consumption itself increases by roughly that amount over the next 25 years. Unless, of course, something is done to change our energy use patterns.
The IEA is an optimist on oil, believing Saudi Arabia can boost production to nearly 20 million barrels per day, and that Iraq, Iran, and several other major producing nations will also be be able to significantly boost production. However, this will only happen with significant capital investment, as the IEA warns oil infrastructure is currently in a state of disrepair. Hence the $20 trillion estimate.
Now, if we really have $20 trillion to spend on energy over the next 25 years, what's actually the best use for that money? I find it very unlikely that spending it on capital for a resource (oil) that will be gone not long after that point is actually an optimal choice. Why does the IEA seem to think so?