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 FriedmanSavage 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. (JEL D11, D91, G11) Acknowledgments We are grateful to Philip H. Dybvig for his helpful suggestions. We also thank Bon Chun Koo for his competent research assistance. This ∗Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China. Email: [email protected]. †Department of Financial Engineering, Ajou University, Suwon 443-749, Republic of Korea. Email: [email protected]. ‡Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China. Email: [email protected].