Almost-sure hedging with permanent price impact

Abergel, F., Loeper, G.: Pricing and hedging contingent claims with liquidity costs and market impact. Available online at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2239498 (2013)

Barles, G.: Solutions de Viscosité des Équations de Hamilton–Jacobi. Springer, Berlin (1994)

Bertsekas, D.P., Shreve, S.E.: Stochastic Optimal Control. The Discrete-Time Case. Academic Press, New York (1978)

Bogachev, V.I., Ruas, M.A.S.: Measure Theory, vol. 1. Springer, Berlin (2007)

Bouchard, B., Elie, R., Touzi, N.: Stochastic target problems with controlled loss. SIAM J. Control Optim. 48, 3123–3150 (2009)

Çetin, U., Jarrow, R.A., Protter, P.: Liquidity risk and arbitrage pricing theory. Finance Stoch. 8, 311–341 (2004)

Çetin, U., Soner, H.M., Touzi, N.: Option hedging for small investors under liquidity costs. Finance Stoch. 14, 317–341 (2010)

Cheridito, P., Soner, H.M., Touzi, N.: The multi-dimensional super-replication problem under gamma constraints. Ann. Inst. Henri Poincaré, C Anal. Non Linéaire 22, 633–666 (2005)

Crauel, H.: Random Probability Measures on Polish Spaces. Stochastics Monographs, vol. 11. CRC Press, Boca Raton (2003)

Frey, R.: Perfect option hedging for a large trader. Finance Stoch. 2, 115–141 (1998)

Ladyzhenskaia, O.A., Solonnikov, V., Ural’tseva, N.N.: Linear and Quasi-Linear Equations of Parabolic Type. Translations of Mathematical Monographs, vol. 23. Am. Math. Soc., Providence (1988)

Lieberman, G.M.: Second Order Parabolic Differential Equations. World Scientific, Singapore (1996)

Liu, H., Yong, J.M.: Option pricing with an illiquid underlying asset market. J. Econ. Dyn. Control 29, 2125–2156 (2005)

Loeper, G.: Option pricing with market impact and non-linear Black and Scholes PDEs. Available online at arXiv:1301.6252 (2013)

Schönbucher, P.J., Wilmott, P.: The feedback effects of hedging in illiquid markets. SIAM J. Appl. Math. 61, 232–272 (2000)

Sircar, K.R., Papanicolaou, G.: Generalized Black–Scholes models accounting for increased market volatility from hedging strategies. Appl. Math. Finance 5, 45–82 (1998)

Soner, H.M., Touzi, N.: Superreplication under gamma constraints. SIAM J. Control Optim. 39, 73–96 (2000)

Soner, H.M., Touzi, N.: Dynamic programming for stochastic target problems and geometric flows. J. Eur. Math. Soc. 4, 201–236 (2002)

Soner, H.M., Touzi, N.: Hedging under gamma constraints by optimal stopping and face-lifting. Math. Finance 17, 59–80 (2007)

Soner, H.M., Touzi, N.: The dynamic programming equation for second order stochastic target problems. SIAM J. Control Optim. 48, 2344–2365 (2009)