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I wanted to understand why the market is incomplete in jump-diffusion models. whereas if we have a model following geometric Brownian motion then we can get a risk-neutral measure and hence a complete market.

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    $\begingroup$ Basically, a market is complete if it includes as many tradable assets as sources of uncertainty (risk). In a GBM (BS) world, the Brownian motion introduces the riskiness and you have one stock to trade this risk $\Rightarrow$ complete market. In a jump diffusion model, you have additional risk (jump frequency and jump size) but still only one stock $\Rightarrow$ incomplete market. The simplest solution is Merton's (1976) approach of simply assuming that there is no jump risk premium (all jump risk is diversifiable). In incomplete markets, there exist infinitely many risk-neutral measures $\endgroup$ – Kevin Jul 10 '20 at 23:20

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