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All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 15 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 15
Number of page(s) 42
DOI https://doi.org/10.1051/cocv/2023089
Published online 01 March 2024
  1. R. Isaacs, Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. John Wiley and Sons, Inc., New York–London–Sydney (1965). [Google Scholar]
  2. L.C. Evans and P.E. Souganidis, Differential games and representation formulas for solutions of Hamilton–Jacobi–Isaacs equations. Indiana Univ. Math. J. 33 (1984) 773–797. [Google Scholar]
  3. R. Aïd, M. Basei, G. Callegaro, L. Campi and T. Vargiolu, Nonzero-sum stochastic differential games with impulse controls: a verification theorem with applications. Math. Oper. Res. (2019) 1–28. [Google Scholar]
  4. A. Cosso, Stochastic differential games involving impulse controls and double-obstacle quasi-variational inequalities. SIAM J. Control Optim. 51 (2013) 2102–2131. [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Basei, Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates. Math. Methods Oper. Res. 89 (2019) 355–383. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Crandall, H. Ishii and P.L. Lions, User’s guide to viscosity solutions of second order partial differential equations. Bui. Am. Math. Soc. 27 (1992) 1–67. [CrossRef] [Google Scholar]
  7. G. Barles, Solutions de viscosité des équations d’Hamilton–Jacobi. Math. Appl. (1994). [Google Scholar]
  8. M. Akian, A. Sulem and M. Taksar, Dynamic optimization of long term growth rate for a portfolio with transaction costs and logarithm utility. Math. Finance 11 (2001) 153–188. [CrossRef] [MathSciNet] [Google Scholar]
  9. V. Ly, Vath, M. Mnif and H. Pham, A model of optimal portfolio selection under liquidity risk and price impact. Finance Stochast. 11 (2007) 51–90. [Google Scholar]
  10. D. Gilbarg, and N. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer Verlag, Berlin (1977). [CrossRef] [Google Scholar]
  11. R. Aïd, F. Bernal, M. Mnif, D. Zabaljauregui and J.P. Zubelli, A policy iteration algorithm for nonzero-sum stochastic impulse games. ESAIM 65 (2019) 27–45. [CrossRef] [EDP Sciences] [Google Scholar]
  12. B. Bouchard, and N. Touzi, Weak dynamic programming principle for viscosity solutions. SIAM J. Control Optim. 49 (2011) 948–962. [CrossRef] [MathSciNet] [Google Scholar]
  13. D. Bertsekas, and S. Shreve, Stochastic optimal control; the discrete-time case. Mathematics in Science and Engineering. Academic Press (1978). [Google Scholar]
  14. H. Soner, Optimal control with state-space constraint, I and II. SIAM J. Cont. Optim. 24 (1986) 552–561, and 1110–1122. [CrossRef] [Google Scholar]
  15. T. Zariphopoulou, Optimal Investment-Consumption Models with Constraints. Ph.D. thesis, Brown University (1988). [Google Scholar]
  16. K. Ishii, Viscosity solutions of nonlinear second order elliptic PDEs associated with impulse control problems. Funkcial. Ekvac. 36 (1993) 123–141. [MathSciNet] [Google Scholar]
  17. G. Pag,és, H. Pham and J. Printems, Optimal quantization methods and applications to numerical problems in finance, edited by S. Rachev. Handbook on Numerical Methods in Finance (2004) 253–298. [Google Scholar]
  18. R. Korn, Portfolio optimization with strictly positive transaction costs and impulse control. Finance Stochast. 2 (1998) 85–114. [CrossRef] [Google Scholar]
  19. J.P. Chancelier, B. Oksendal and A. Sulem, Combined stochastic control and optimal stopping, and application to numerical approximation of combined stochastic and impulse control. Edited by A. Shiryaev. Stochastic Financial Mathematics, Proc. Steklov Math. Inst. Moscou. (2001) 149–175. [Google Scholar]
  20. M. Ga,ïgi, V. Ly Vath, M. Mnif and S. Toumi, Numerical approximation for a portfolio optimization problem under liquidity risk and costs. Appl. Math. Optim. 74 (2016) 163–195. [CrossRef] [MathSciNet] [Google Scholar]
  21. B. Øksendal, Stochastic Differential Equations. Springer-Verlag, Berlin (2003). [CrossRef] [Google Scholar]
  22. G. Pag,és and H. Luschgy, Functional quantization of a class of Brownian diffusions: a constructive approach. Stoch. Process. Appl. 116 (2006) 310–336. [CrossRef] [Google Scholar]
  23. G. Pag,és and H. Luschgy, Functional quantization of Gaussian Process. J. Funct. Anal. 196 (2002) 486–531. [Google Scholar]

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