A central issue that is discussed in climate policy is the fear of owners of stocks of fossil hydrocarbon deposits that high CO2 taxes and bans on the combustion use of hydrocarbons will turn their stocks into stranded assets. They might react by extracting and selling their reserves today: a rush to burn results. We show how the stranded-asset problem could be avoided or strongly moderated. We analyze a simple intertemporal equilibrium with a given stock of fossil hydrocarbons. In this framework the following properties hold: For a climate-neutral solution to the rush-to-burn problem it is important to maintain existing and generate new markets for climate-neutral products from fossil hydrocarbons in the future, where we give examples for such products. Subsidies for such products (or for their innovation) reduce the rush-to-burn problem. In contrast, the creation of substitutes for fossil hydrocarbon-based climate-neutral products, or subsidies for such products reduce the market for products made from fossil hydrocarbons. This can aggravate the stranded-assets problem and thus can have a climate-damaging effect.