Hey what is the easiest way to find equivalent martingale measure for Levy processes (in Merton model and Kou model for example)? I would like to write the dynamics of the stock price process under the martingale measure but I do not know how to find it. Kou 2002 proposed utility maximalization approach but I would like to find easiest way.

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    $\begingroup$ If jumps are present, markets are incomplete with infinitely many EMMs. You can accept this and implement some superhedging or minimum-variance hedging. If you may want to choose a specific EMM to get a unique price, you need to specify the market price of jump risk. Merton (1976) avoids this issue by assuming this risk diversifiable. You however normally need some economic argument (Kou) to justify your choice, or minimise hedging errors (Bergomi), see these great answers from ir7 and Quantuple. $\endgroup$ – Kevin Aug 30 '20 at 14:02

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