Investment, Consumption and Hedging under Incomplete Markets

Entrepreneurs often face undiversi¯able idiosyncratic risks from their business invest- ments. Motivated by this observation, we extend the standard real options approach to investment to an incomplete markets environment and analyze the joint decisions of busi- ness investments, consumption-saving and portfolio selection. Our analysis depends cru- cially on whether the investment payo®s are in lump-sum or in °ows. Precautionary saving e®ect plays a key role. In the lump-sum payo® case, risk aversion accelerates investment. Moreover, when the agent's precautionary motive is strong enough, an increase in volatility accelerates investment. These results may be reversed for the °ow payo® case. Finally, hedging a®ects investment decisions by changing the expected growth of wealth and reduc- ing the agent's exposure to idiosyncratic risk. The agent's hedging demand is higher when he is closer to exercising the investment option.