Soner, H. Mete; Touzi, Nizar Hedging under gamma constraints by optimal stopping and face-lifting. (English) Zbl 1278.91151 Math. Finance 17, No. 1, 59-79 (2007). Summary: A super-replication problem with a gamma constraint, introduced in [the authors, SIAM J. Control Optimization 39, No. 1, 73–96 (2000; Zbl 0960.91036)], is studied in the context of the one-dimensional Black-Scholes model. Several representations of the minimal super-hedging cost are obtained using the characterization derived in [P. Cheridito and the authors, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 22, No. 5, 633–666 (2005; Zbl 1078.91010); Ann. Appl. Probab. 15, No. 4, 2472–2495 (2005; Zbl 1099.60027)]. It is shown that the upper bound constraint on the gamma implies that the optimal strategy consists in hedging a conveniently face-lifted payoff function. Further an unusual connection between an optimal stopping problem and the lower bound is proved. A formal description of the optimal hedging strategy as a succession of periods of classical Black-Scholes hedging strategy and simple buy-and-hold strategy is also provided. Cited in 1 ReviewCited in 4 Documents MSC: 91G10 Portfolio theory 91G80 Financial applications of other theories 93E20 Optimal stochastic control Keywords:hedging under constraints; stochastic control; optimal stopping Citations:Zbl 0960.91036; Zbl 1078.91010; Zbl 1099.60027 PDFBibTeX XMLCite \textit{H. M. Soner} and \textit{N. Touzi}, Math. Finance 17, No. 1, 59--79 (2007; Zbl 1278.91151) Full Text: DOI