Investment, consumption and hedging with lump-sum payoff in finite horizon under incomplete market

Abstract

Entrepreneurs often face undiversifiable idiosyncratic risks from their business investment. This paper analyses the joint decisions of investment, consumption/savings and portfolio selection in the models with lump-sum payoffs in finite horizon under incomplete markets. It shows that the optimal exercising boundary is decreasing w.r.t. and continuous in . Moreover, the free boundary is smooth. When the agent can trade a risky asset to partially hedge against investment risk, this ability will make the agent better off relative to the self-insurance setting. The main contribution of this paper is to generalize the results with respect to infinite horizon in Miao and Wang (2007) to the finite horizon case by PDE technique.

Keywords:

• free boundary problem
• investment and consumption
• lump-sum payoff
• finite horizon
• incomplete market

AMS Subject Classifications:

• 35R35
• 60G40
• 91B70
• 93E20

Acknowledgments

The project is supported by National Natural Science Foundation of China (No.11271143 and No. 10901060) and National Natural Science Foundation of GuangDong province (No.9451063101002091).