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Moderate deviation for maximum likelihood estimators from single server queues
Limit behaviour of the minimal solution of a BSDE with singular terminal condition in the non Markovian setting
Laboratoire Manceau de Mathématiques, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans cedex 9, France |
References:
[1] |
Ankirchner, S., M. Jeanblanc, and T. Kruse. (2014). BSDEs with Singular Terminal Condition and a Control Problem with Constraints, SIAM J. Control Optim. 52, no. 2, 893–913., |
[2] |
Bank, P. and M. Voß. (2018). Linear quadratic stochastic control problems with stochastic terminal constraint, SIAM J. Control Optim. 56, no. 2, 672–699., |
[3] |
Bouchard, B., D. Possamaï, X. Tan, and C. Zhou. (2018). A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations, Ann. Inst. Henri Poincaré, Probab. Stat. 54, no. 1, 154–172., |
[4] |
Cont, R. (2016). Functional Itô calculus and functional Kolmogorov equations, Birkhäuser/Springer, CRM Barcelona., |
[5] |
Cont, R. and D.-A. Fournié. (2010). A functional extension of the Ito formula, C. R. Math. Acad. Sci. Paris. 348, no. 1–2, 57–61., |
[6] |
Cont, R. and D.-A. Fournié. (2013). Functional Itô calculus and stochastic integral representation of martingales, Ann. Probab. 41, no. 1, 109–133., |
[7] |
Cont, R. and Y. Lu. (2016). Weak approximation of martingale representations, Stoch. Process. Appl. 126, no. 3, 857–882., |
[8] |
Dellacherie, C. and P.-A. Meyer. (1980). Probabilités et potentiel. Théorie des martingales, Chapitres V à VIII, Hermann., |
[9] |
Delong, Ł. (2013). Backward stochastic differential equations with jumps and their actuarial and financial applications, European Actuarial Academy (EAA) Series, Springer, London. BSDEs with jumps., |
[10] |
Dupire, B. (2009). Functional Itô calculus, Bloomberg Portfolio Research Paper No 2009-04-FRONTIERS., |
[11] |
Graewe, P., U. Horst, and J. Qiu. (2015). A non-Markovian liquidation problem and backward SPDEs with singular terminal conditions, SIAM J. Control Optim. 53, no. 2, 690–711., |
[12] |
Kruse, T. and A. Popier. (2016). BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration, Stochastics 88, no. 4, 491–539., |
[13] |
Kruse, T. and A. Popier. (2016). Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting, Stoch. Process. Appl. 126, no. 9, 2554–2592., |
[14] |
Kruse, T. and A. Popier. (2017). Lp-solution for BSDEs with jumps in the case p < 2: corrections to the paper ‘BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration, Stochastics 89, no. 8, 1201–1227., |
[15] |
Pardoux, E. and A. Rascanu. (2014). Stochastic Differential Equations, Backward SDEs, Partial Differential Equations, volume 69 of Stochastic Modelling and Applied Probability, Springer-Verlag. https://doi.org/10.1007/978-3-319-05714-9., |
[16] |
Popier, A. (2006). Backward stochastic differential equations with singular terminal condition, Stoch.Process. Appl 116, no. 12, 2014–2056., |
[17] |
Popier, A. (2016). Limit behaviour of bsde with jumps and with singular terminal condition, ESAIM: PS 20, 480–509., |
[18] |
Protter, P.E. (2004). Stochastic integration and differential equations, volume 21 of Applications of Mathematics (New York), second edition, Springer-Verlag, Berlin. Stochastic Modelling and Applied Probability., |
[19] |
Quenez, M.-C. and A. Sulem. (2013). BSDEs with jumps, optimization and applications to dynamic risk measures, Stoch. Process. Appl. 123, no. 8, 3328–3357., |
[20] |
Sezer, A.D., T. Kruse, and A. Popier. (2019). Backward stochastic differential equations with nonMarkovian singular terminal values, Stoch. Dyn. 19, no. 2, 1950006., |
show all references
References:
[1] |
Ankirchner, S., M. Jeanblanc, and T. Kruse. (2014). BSDEs with Singular Terminal Condition and a Control Problem with Constraints, SIAM J. Control Optim. 52, no. 2, 893–913., |
[2] |
Bank, P. and M. Voß. (2018). Linear quadratic stochastic control problems with stochastic terminal constraint, SIAM J. Control Optim. 56, no. 2, 672–699., |
[3] |
Bouchard, B., D. Possamaï, X. Tan, and C. Zhou. (2018). A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations, Ann. Inst. Henri Poincaré, Probab. Stat. 54, no. 1, 154–172., |
[4] |
Cont, R. (2016). Functional Itô calculus and functional Kolmogorov equations, Birkhäuser/Springer, CRM Barcelona., |
[5] |
Cont, R. and D.-A. Fournié. (2010). A functional extension of the Ito formula, C. R. Math. Acad. Sci. Paris. 348, no. 1–2, 57–61., |
[6] |
Cont, R. and D.-A. Fournié. (2013). Functional Itô calculus and stochastic integral representation of martingales, Ann. Probab. 41, no. 1, 109–133., |
[7] |
Cont, R. and Y. Lu. (2016). Weak approximation of martingale representations, Stoch. Process. Appl. 126, no. 3, 857–882., |
[8] |
Dellacherie, C. and P.-A. Meyer. (1980). Probabilités et potentiel. Théorie des martingales, Chapitres V à VIII, Hermann., |
[9] |
Delong, Ł. (2013). Backward stochastic differential equations with jumps and their actuarial and financial applications, European Actuarial Academy (EAA) Series, Springer, London. BSDEs with jumps., |
[10] |
Dupire, B. (2009). Functional Itô calculus, Bloomberg Portfolio Research Paper No 2009-04-FRONTIERS., |
[11] |
Graewe, P., U. Horst, and J. Qiu. (2015). A non-Markovian liquidation problem and backward SPDEs with singular terminal conditions, SIAM J. Control Optim. 53, no. 2, 690–711., |
[12] |
Kruse, T. and A. Popier. (2016). BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration, Stochastics 88, no. 4, 491–539., |
[13] |
Kruse, T. and A. Popier. (2016). Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting, Stoch. Process. Appl. 126, no. 9, 2554–2592., |
[14] |
Kruse, T. and A. Popier. (2017). Lp-solution for BSDEs with jumps in the case p < 2: corrections to the paper ‘BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration, Stochastics 89, no. 8, 1201–1227., |
[15] |
Pardoux, E. and A. Rascanu. (2014). Stochastic Differential Equations, Backward SDEs, Partial Differential Equations, volume 69 of Stochastic Modelling and Applied Probability, Springer-Verlag. https://doi.org/10.1007/978-3-319-05714-9., |
[16] |
Popier, A. (2006). Backward stochastic differential equations with singular terminal condition, Stoch.Process. Appl 116, no. 12, 2014–2056., |
[17] |
Popier, A. (2016). Limit behaviour of bsde with jumps and with singular terminal condition, ESAIM: PS 20, 480–509., |
[18] |
Protter, P.E. (2004). Stochastic integration and differential equations, volume 21 of Applications of Mathematics (New York), second edition, Springer-Verlag, Berlin. Stochastic Modelling and Applied Probability., |
[19] |
Quenez, M.-C. and A. Sulem. (2013). BSDEs with jumps, optimization and applications to dynamic risk measures, Stoch. Process. Appl. 123, no. 8, 3328–3357., |
[20] |
Sezer, A.D., T. Kruse, and A. Popier. (2019). Backward stochastic differential equations with nonMarkovian singular terminal values, Stoch. Dyn. 19, no. 2, 1950006., |
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