Pathwise no-arbitrage in a class of Delta hedging strategies

Acciaio, B, Beiglböck, M, Penkner, F, Schachermayer, W: A model-free version of the fundamental theorem of asset pricing and the super-replication theorem. Math. Finance. 26(2), 233–251 (2016). doi: 10.1111/mafi.12060 .

Alvarez, A, Ferrando, S, Olivares, P: Arbitrage and hedging in a non probabilistic framework. Math. Financ. Econ. 7(1), 1–28 (2013). doi: 10.1007/s11579-012-0074-5 .

Beiglböck, M, Cox, AM, Huesmann, M, Perkowski, N, Prömel, DJ: Pathwise super-replication via Vovk’s outer measure (2015). http://arxiv.org/abs/1504.03644 .

Bender, C, Sottinen, T, Valkeila, E: Pricing by hedging and no-arbitrage beyond semimartingales. Finance Stoch. 12(4), 441–468 (2008). doi: 10.1007/s00780-008-0074-8 .

Biagini, S, Bouchard, B, Kardaras, C, Nutz, M: Robust fundamental theorem for continuous processes. Mathematical Finance (2015). doi: 10.1111/mafi.12110 .

Bick, A, Willinger, W: Dynamic spanning without probabilities. Stochastic Process. Appl. 50(2), 349–374 (1994). doi: 10.1016/0304-4149(94)90128-7 .

Bouchard, B, Nutz, M: Arbitrage and duality in nondominated discrete-time models. Ann. Appl. Probab. 25(2), 823–859 (2015). doi: 10.1214/14-AAP1011 .

Bühler, H: Pricing with a discrete smile (2015). SSRN preprint 2642630 http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2642630 .

Cont, R, Fournié, D-A: Change of variable formulas for non-anticipative functionals on path space. J. Funct. Anal. 259(4), 1043–1072 (2010). doi: 10.1016/j.jfa.2010.04.017 .

Davis, M, Obłój, J, Raval, V: Arbitrage bounds for prices of weighted variance swaps. Math. Finance. 24(4), 821–854 (2014). doi: 10.1111/mafi.12021 .

Dudley, RM: Wiener functionals as Itô integrals. Ann. Probability. 5(1), 140–141 (1977).

Dupire, B: Pricing and hedging with smiles. In: Mathematics of Derivative Securities (Cambridge, 1995), Publ. Newton Inst, pp. 103–111. Cambridge Univ. Press, Cambridge (1997).

Dupire, B: Functional Itô calculus. Bloomberg Portfolio Research Paper (2009).

El Karoui, N, Jeanblanc-Picqué, M, Shreve, SE: Robustness of the Black and Scholes formula. Math. Finance. 8(2), 93–126 (1998). doi: 10.1111/1467-9965.00047 .

Föllmer, H: Calcul d’Itô sans probabilités. In: Seminar on Probability, XV (Univ. Strasbourg, Strasbourg, 1979/1980), Lecture Notes in Math, pp. 143–150. Springer, Berlin (1981).

Föllmer, H: Probabilistic aspects of financial risk. In: European Congress of Mathematics, Vol. I (Barcelona, 2000), Progr. Math, pp. 21–36. Birkhäuser, Basel (2001).

Föllmer, H, Schied, A: Stochastic Finance. An Introduction in Discrete Time. 3rd ed. Walter de Gruyter & Co., Berlin (2011).

Freedman, D: Brownian Motion and Diffusion. 2nd ed. Springer, New York (1983).

Hobson, D: The Skorokhod embedding problem and model-independent bounds for option prices. In: Paris-Princeton Lectures on Mathematical Finance 2010, Lecture Notes in Math, pp. 267–318. Springer (2011), doi: 10.1007/978-3-642-14660-2_4 http://dx.doi.org/10.1007/978-3-642-14660-2_4 .

Hobson, DG: Robust hedging of the lookback option. Finance Stoch. 2(4), 329–347 (1998).

Janson, S, Tysk, J: Preservation of convexity of solutions to parabolic equations. J. Differential Equations. 206(1), 182–226 (2004). doi: 10.1016/j.jde.2004.07.016 .

Jeanblanc, M, Yor, M, Chesney, M: Mathematical Methods for Financial Markets. Springer Finance. Springer (2009).

Ji, S, Yang, S: Classical solutions of path-dependent PDEs and functional forward-backward stochastic systems. Math. Probl. Eng, 423101–11 (2013). downloads.hindawi.com/journals/mpe/2013/423101.pdf .

Lyons, TJ: Uncertain volatility and the risk-free synthesis of derivatives. Appl. Math. Finance. 2(2), 117–133 (1995).

Peng, S, Wang, F: BSDE, path-dependent PDE and nonlinear Feynman-Kac formula. F. Sci. China Math. 59, 19 (2016). doi: 10.1007/s11425-015-5086-1 .

Riedel, F: Financial economics without probabilistic prior assumptions. Decisions Econ. Finan. 38, 75–91 (2015). doi: 10.1007/s10203-014-0159-0 .

Schied, A: Model-free CPPI. J. Econom. Dynam. Control. 40, 84–94 (2014). doi: 10.1016/j.jedc.2013.12.010 .

Schied, A: On a class of generalized Takagi functions with linear pathwise quadratic variation. J. Math. Anal. Appl. 433, 974–990 (2016).

Schied, A, Stadje, M: Robustness of delta hedging for path-dependent options in local volatility models. J. Appl. Probab. 44(4), 865–879 (2007). doi: 10.1239/jap/1197908810 .

Schied, A, Voloshchenko, I: The associativity rule in pathwise functional Itô calculus (2016). http://arxiv.org/abs/1605.08861 .

Schied, A, Speiser, L, Voloshchenko, I: Model-free portfolio theory and its functional master formula (2016). arXiv preprint 1606.03325.

Sondermann, D: Introduction to Stochastic Calculus for Finance. Lecture Notes in Economics and Mathematical Systems, Vol. 579. Springer, Berlin (2006).

Stroock, DW, Varadhan, SRS: Diffusion processes with continuous coefficients. Comm. Pure Appl. Math. 22, 345–400479530 (1969).

Stroock, DW, Varadhan, SRS: On the support of diffusion processes with applications to the strong maximum principle. In: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, pp. 333–359. Univ. California Press, Berkeley, Calif (1972).

Vovk, V: Rough paths in idealized financial markets. Lith. Math. J. 51(2), 274–285 (2011). doi: 10.1007/s10986-011-9125-5 .

Vovk, V: Continuous-time trading and the emergence of probability. Finance Stoch. 16(4), 561–609 (2012). doi: 10.1007/s00780-012-0180-5 .

Vovk, V: Itô calculus without probability in idealized financial markets. Lith. Math. J. 55(2), 270–290 (2015). doi: 10.1007/s10986-015-9280-1 .

Widder, DV: The Heat Equation. Pure and Applied Mathematics, Vol. 67, pp. 267, New York and London (1975).