We propose an analytically tractable continuous-time model of experimentation in which a risk-averse entrepreneur cannot fully diversify the idiosyncratic risk from his business investment. He makes consumption/savings and business exit decisions jointly, while learning about the unknown quality of the project over time. Using the closed-form solutions, we show that (i) the entrepreneur may stay in business even though the project's net present value (NPV) is negative; (ii) entrepreneurial risk aversion erodes option value and lowers private project value so that a sufficiently risk-averse entrepreneur may exit even when the NPV is positive; (iii) a more risk-averse or a more pessimistic entrepreneur exits earlier; and (iv) the model can generate a positive relation between wealth and entrepreneurial survival duration from undiversifiable idiosyncratic risk without liquidity constraints.
Wang, Neng, and Jianjun Miao. "Experimentation under Uninsurable Idiosyncratic Risk: An Application to Entrepreneurial Survival." Working paper, Columbia Business School, 2007.
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