A Friedman-Savage Consumer Almost Gambles : A Continuous Time Model of Consumption and Investment with Non-Concave Utility

We examine the consumption and portfolio decisions of an agent with Friedman-Savage type period utility in continuous time. We find the Friedman-Savage consumer does not gamble, but will aggressively invest in risky activities for wealth levels that support a minimum subsistence level of consumption. As the market premium of risk approaches zero, the agent becomes infinitely aggressive for these wealth levels. Also, there will be a jump in consumption corresponding to the region where the utility is convex. Last, the agent becomes more aggressive as patience decreases