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ROBUST UTILITY MAXIMIZATION WITH LÉVY PROCESSES
Author(s) -
NEUFELD ARIEL,
NUTZ MARCEL
Publication year - 2018
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12139
Subject(s) - utility maximization , saddle point , lévy process , volatility (finance) , logarithm , mathematical optimization , portfolio , economics , maximization , investment strategy , portfolio optimization , jump , utility maximization problem , mathematical economics , econometrics , mathematics , financial economics , microeconomics , mathematical analysis , physics , geometry , quantum mechanics , profit (economics)
We study a robust portfolio optimization problem under model uncertainty for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible Lévy triplets, that is, possible instantaneous drift, volatility, and jump characteristics of the price process. We show that an optimal investment strategy exists and compute it in semi‐closed form. Moreover, we provide a saddle point analysis describing a worst‐case model.