Open Access
Volume 30, 2024
Article Number 29
Number of page(s) 25
Published online 12 April 2024
  1. P. Barrieu and N. El Karoui, Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs. Ann. Probab. 41 (2013) 1831–1863. [Google Scholar]
  2. P. Briand and Y. Hu, Quadratic BSDEs with convex generators and unbounded terminal conditions. Probab. Theory Related Fields 141 (2008) 543–567. [Google Scholar]
  3. F. Delbaen, Y. Hu, and A. Richou, On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions. Ann. Inst. Henri Poincaré Probab. Stat. 47 (2011) 559–574. [Google Scholar]
  4. Y. Hu and S. Tang, Multi-dimensional backward stochastic differential equations of diagonally quadratic generators. Stochastic Process. Appl. 126 (2016) 1066–1086. [Google Scholar]
  5. M. Kobylanski, Backward stochastic differential equations and partial differential equations with quadratic growth. Ann. Probab. 28 (2000) 558–602. [Google Scholar]
  6. R. Tevzadze, Solvability of backward stochastic differential equations with quadratic growth, Stoch. Process. Appl. 118 (2008) 503–515. [Google Scholar]
  7. H. Xing and G. Žitković, A class of globally solvable Markovian quadratic BSDE systems and applications. Ann. Probab. 46 (2018) 491–550. [Google Scholar]
  8. J.-M. Bismut, Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim. 14 (1976) 419–444. [Google Scholar]
  9. F. Delbaen, P. Grandits, T. Rheinländer, D. Samperi, M. Schweizer and C. Stricker, Exponential hedging and entropic penalties. Math. Finance 12 (2002) 99–123. [Google Scholar]
  10. Y. Hu, P. Imkeller and M. Müller, Utility maximization in incomplete markets. Ann. Appl. Probab. 15 (2005) 1691–1712. [Google Scholar]
  11. N. El Karoui, and S. Hamadène, BSDEs and risk-sensitive control, zero-sumand nonzero-sum game problems of stochastic functional differential equations. Stochastic Process. Appl. 107 (2003) 145–169. [Google Scholar]
  12. A.E.B. Lim and X. Zhou, A new risk-sensitive maximum principle. IEEE Trans. Automat. Control 50 (2005) 958–966. [Google Scholar]
  13. J. Moon, Generalized risk-sensitive optimal control and Hamilton–Jacobi–Bellman equation. IEEE Trans. Automat. Control 66 (2021) 2319–2325. [Google Scholar]
  14. C. Skiadas, Robust control and recursive utility. Finance Stoch. 7 (2003) 475–489. [Google Scholar]
  15. W. Faidi, A. Matoussi and M. Mnif, Maximization of recursive utilities: a dynamic maximum principle approach. SIAM J. Financial Math. 2 (2011) 1014–1041. [Google Scholar]
  16. J. Yong, Optimality variational principle for controlled forward-backward stochastic differential equations with mixed initialterminal conditions. SIAM J. Control Optim. 48 (2010) 4119–4156. [Google Scholar]
  17. Y. Hu and S. Peng, Solution of forward-backward stochastic differential equations. Probab. Theory Related Fields 103 (1995) 273–283. [Google Scholar]
  18. J. Ma, P. Protter and J. Yong, Solving forward–backward stochastic differential equations explicitly – a 4 step scheme. Probab. Theory Related Fields 98 (1994) 339–359. [Google Scholar]
  19. J. Ma, Z. Wu, D. Zhang and J. Zhang, On well-posedness of forward–backward SDEs – a unified approach. Ann. Appl. Probab. 25 (2015) 2168–2214. [Google Scholar]
  20. A. Lazrak and M.C. Quenez, A generalized stochastic differential utility. Math. Oper. Res. 28 (2003) 154–180. [Google Scholar]
  21. T.R. Bielecki, H. Jin, S.R. Pliska and X. Zhou, Continuous time mean variance portfolio selection with bankruptcy prohibition. Math. Finance 15 (2005) 213–244. [Google Scholar]
  22. N. El Karoui, S. Peng and M.C. Quenez, A dynamic maximum principle for the optimization of recursive utilities under constraints. Ann. Appl. Probab. 11 (2001) 664–693. [Google Scholar]
  23. S. Ji and X. Zhou, A generalized Neyman-Pearson lemma for g-probabilities. Probab. Theory Related Fields 148 (2010) 645–669. [Google Scholar]
  24. S. Peng, A general stochastic maximum principle for optimal control problems. SIAM J. Control Optim. 28 (1990) 966–979. [Google Scholar]
  25. M. Hu, S. Ji and X. Xue, A global stochastic maximum principle for fully coupled forward-backward stochastic systems. SIAM J. Control Optim. 56 (2018) 4309–4335. [Google Scholar]
  26. S. Peng, Backward stochastic differential equations and applications to optimal control. Appl. Math. Optim. 27 (1993) 125–144. [Google Scholar]
  27. Z. Wu, A general maximum principle for optimal control of forward-backward stochastic systems. Automatica 49 (2013) 1473–1480. [Google Scholar]
  28. S. Ji and S. Peng, Terminal perturbation method for the backward approach to continuous time mean-variance portfolio selection, Stochastic Process. Appl. 118 (2008) 952–967. [Google Scholar]
  29. S. Ji and X. Zhou, A maximum principle for stochastic optimal optimal control with terminal state constraints and its applications. Commun. Inf. Syst. 6 (2006) 321–337. [Google Scholar]
  30. S. Ji and Q. Wei, A maximum principle for fully coupled forward-backward stochastic control systems with terminal state constraints. J. Math. Anal. Appl. 407 (2013) 200–210. [Google Scholar]
  31. Q. Wei, Stochastic maximum principle for mean-field forward–backward stochastic control system with terminal state constraints. Sci. China Math. 59 (2016) 809–822. [Google Scholar]
  32. P. Briand and F. Confortola, BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces. Stochastic Process. Appl. 118 (2008) 818–838. [Google Scholar]
  33. N. Kazamaki, Continuous Exponential Martingales and BMO. Springer-Verlag Berlin Heidelberg (1994). [Google Scholar]
  34. N. El Karoui, S. Peng and M.C. Quenez, Backward stochastic differential equations in finance. Math. Finance 7 (1997) 1–71. [Google Scholar]
  35. I. Ekeland, On the variational principle. J. Math. Anal. Appl. 47 (1974) 324–353. [Google Scholar]
  36. I.L. Gal’Chuk, Existence and uniqueness of a solution for stochastic equations with respect to semimartingales. Theory Probab. Appl. 23 (1978) 751–763. [Google Scholar]
  37. S. Tang, General linear quadratic optimal stochastic control problems with random coefficients: linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim. 42 (2003) 53–75. [Google Scholar]
  38. P. Billingsley, Probability and Measure, 2nd edn. John Wiley & and Sons, Canada (1986). [Google Scholar]
  39. R.M. Dudley, Real Analysis and Probability. The Press Syndicate of the University of Cambridge, United Kingdom (2004). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.