|
[1]
|
F. Abergel and G. Loeper, Option pricing and hedging with liquidity costs and market impact, Econophysics and Sociophysics: Recent Progress and Future Directions, Abergel, F. et al., eds. New Economic Windows. Springer, Cham, 2017, 19-40.
doi: 10.1007/978-3-319-47705-3_2.
|
|
[2]
|
D. G. Aronson and Ph. Bénilan, Régularité des solutions de l'équation des milieux poreux dans $\mathbb{R}^N$, C. R. Acad. Sci. Paris Sér. A-B, 288 (1979), A103-A105.
|
|
[3]
|
Ph. Bénilan and K. Ha, Équation d'évolution du type $(du/dt)+\beta \upsilon \phi(u)\ni0$ dans $L^{\infty }(U)$, C. R. Acad. Sci. Paris Sér. A-B, 281 (1975), A947-A950.
|
|
[4]
|
F. Bernis, J. Hulshof and J. L. Vázquez, A very singular solution for the dual porous medium equation and the asymptotic behaviour of general solutions, J. Reine Angew. Math., 435 (1993), 1-31.
doi: 10.1515/crll.1993.435.1.
|
|
[5]
|
B. Bouchard, G. Loeper, H. M. Soner and Ch. Zhou, Second-order stochastic target problems with generalized market impact, SIAM J. Control Optim., 57 (2019), 4125-4149.
doi: 10.1137/18M1196078.
|
|
[6]
|
B. Bouchard, G. Loeper and Y. Zou, Almost-sure hedging with permanent price impact, Finance Stoch., 20 (2016), 741-771.
doi: 10.1007/s00780-016-0295-1.
|
|
[7]
|
B. Bouchard, G. Loeper and Y. Zou, Hedging of covered options with linear market impact and gamma constraint, SIAM J. Control Optim., 55 (2017), 3319-3348.
doi: 10.1137/15M1054109.
|
|
[8]
|
M. Crandal and M. Pierre, Regularizing effects for $u_{t}+A\varphi (u) = 0$ in $L^{1}$, J. Funct. Anal., 45 (1982), 194-212.
doi: 10.1016/0022-1236(82)90018-0.
|
|
[9]
|
M. G. Crandal and M. Pierre, Regularizing effects for $u_{t} = \Delta \varphi (u)$, Trans. Amer. Math. Soc., 274 (1982), 159-168.
doi: 10.1090/S0002-9947-1982-0670925-4.
|
|
[10]
|
B. E. J. Dahlberg and C. E. Kenig, Weak solutions of the porous medium equation in a cylinder, Trans. Amer. Math. Soc., 336 (1993), 701-709.
doi: 10.1090/S0002-9947-1993-1085940-6.
|
|
[11]
|
G. Díaz and I. Díaz, Finite extinction time for a class of nonlinear parabolic equations, Comm. Partial Differential Equations, 4 (1979), 1213-1231.
doi: 10.1080/03605307908820126.
|
|
[12]
|
E. DiBenedetto, U. Gianazza and V. Vespri, Harnack's Inequality for Degenerate and Singular Parabolic Equations, Springer Monographs in Mathematics. Springer, New York, 2012.
doi: 10.1007/978-1-4614-1584-8.
|
|
[13]
|
G. Duvaut and J.-L. Lions, Les Inéquations en Mécanique et en Physique, Travaux et Recherches Mathématiques, No. 21. Dunod, Paris, 1972.
|
|
[14]
|
A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Inc., Englewood Cliffs, N. J. 1964.
|
|
[15]
|
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2001.
|
|
[16]
|
I. Guo and G. Loeper, Path dependent optimal transport and model calibration on exotic derivatives, Ann. Appl. Probab., 31 (2021), 1232-1263.
doi: 10.1214/20-aap1617.
|
|
[17]
|
I. Guo, G. Loeper and Sh. Wang, Local volatility calibration by optimal transport, 2017 MATRIX Annals, MATRIX Book Ser., 2, Springer, Cham, 2019, 51-64
|
|
[18]
|
K. S. Ha, Sur des semi-groupes non linéaires dans les espaces $L^\infty(\Omega)$, J. Math. Soc. Japan, 31 (1979), 593-622.
doi: 10.2969/jmsj/03140593.
|
|
[19]
|
S. L. Kamenomostskaja, On Stefan's problem(Russian), Mat. Sb. (N.S.), 53 (1961), 489-514.
|
|
[20]
|
Y. Konishi, On the nonlinear semi-groups associated with $u_t = \Delta \beta(u)$ and $\varphi(u_t) = \Delta u$, J. Math. Soc. Japan, 25 (1973), 622-628.
doi: 10.2969/jmsj/02540622.
|
|
[21]
|
J. Li, J. Yin, J. Sun and Zh. Guo, A weighted dual porous medium equation applied to image restoration, Math. Methods Appl. Sci., 36 (2013), 2117-2127.
doi: 10.1002/mma.2739.
|
|
[22]
|
P.-L. Lions, Some problems related to the Bellman-Dirichlet equation for two operators, Comm. Partial Differential Equations, 5 (1980), 753-771.
doi: 10.1080/03605308008820153.
|
|
[23]
|
G. Loeper, Option pricing with linear market impact and nonlinear Black-Scholes equations, Ann. Appl. Probab., 28 (2018), 2664-2726.
doi: 10.1214/17-AAP1367.
|
|
[24]
|
G. Schimperna, A. Segatti and U. Stefanelli, Well-posedness and long-time behavior for a class of doubly nonlinear equations, Discrete Contin. Dyn. Syst., 18 (2007), 15-38.
doi: 10.3934/dcds.2007.18.15.
|
|
[25]
|
W. A. Strauss, Evolution equations non-linear in the time derivative, J. Math. Mech., 15 (1966), 49-82.
|
|
[26]
|
X. Tan and N. Touzi, Optimal transportation under controlled stochastic dynamics, Ann. Probab., 41 (2013), 3201-3240.
doi: 10.1214/12-AOP797.
|
|
[27]
|
J. L. Vázquez, The Porous Medium Equation. Mathematical Theory, Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, Oxford, 2007.
|
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