Investment decisions under incomplete markets in the presence of wealth effects

This paper investigates the impact of market incompleteness on investment decisions. In contrast to previous studies, we assume an entrepreneur has power utility and investment causes an additive increase in her wealth. By using the binomial theorem, we derive the analytical solutions for the option value and investment threshold. First, we show that an increase in wealth alleviates the over-investment problem caused by the market incompleteness. In addition, the marginal value of wealth is always more than one and decreases in the wealth level. Finally, the increase in wealth substantially enhances the value of the investment option and lowers the idiosyncratic risk premium.