2009/12/17 by Jan Kallsen, Kallsen, Jan, Johannes Muhle-Karbe +3
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR) #math.OC #math.PR #q-fin.PM
paper · pdf · doi:10.48550/arxiv.0912.3362
32 pages, 4 figures, to appear in "Mathematics and Financial Economics"
arxiv created 2013/01/08 · arxiv updated 2013/01/09
Kramkov and Sirbu (2006, 2007) have shown that first-order approximations of power utility-based prices and hedging strategies can be computed by solving a mean-variance hedging problem under a specific equivalent martingale measure and relative to a suitable numeraire. In order to avoid the introduction of an additional state variable necessitated by the change of numeraire, we propose an alternative representation in terms of the original numeraire. More specifically, we characterize the relevant quantities using semimartingale characteristics similarly as in Cerny and Kallsen (2007) for mean-variance hedging. These results are illustrated by applying them to exponential Lévy processes and stochastic volatility models of Barndorff-Nielsen and Shephard type.