A tractable model of precautionary saving in continuous time

This letter derives an analytical solution to the following saving problem. An individual chooses the path of consumption that maximises a time-separable von Neumann-Morgenstern utility function, subject to a standard intertemporal budget constraint. Labour income follows a Poisson process. The consumer is both 'prudent' and 'impatient', and accumulates financial wealth as a buffer against the risk of income loss.