Abstract
We give a sufficient condition to identify the q-optimal signed and the q-optimal absolutely continuous martingale measures in exponential Lévy models. As a consequence, we find that in the one-dimensional case, the q-optimal equivalent martingale measures may exist only if the tails for upward jumps are extraordinarily light. Moreover, we derive the convergence of q-optimal signed, resp. absolutely continuous, martingale measures to the minimal entropy martingale measure as q approaches one. Finally, some implications for portfolio optimization are discussed.
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C.N. gratefully acknowledges financial support by UniCredit, Markets and Investment Banking. However, this paper does not reflect the opinion of UniCredit, Markets and Investment Banking, it is the personal view of the authors.
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Bender, C., Niethammer, C.R. On q-optimal martingale measures in exponential Lévy models. Finance Stoch 12, 381–410 (2008). https://doi.org/10.1007/s00780-008-0067-7
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DOI: https://doi.org/10.1007/s00780-008-0067-7