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Volumn 1, Issue 1, 2016, Pages

Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications

(1)  Pham, Huyên a,b  

a CNRS   (France)
b CREST   (France)

Author keywords

Backward stochastic differential equation; Dynamic programming; Linear quadratic optimal control; Random coefficients; Riccati equation; Stochastic McKean Vlasov SDEs

Indexed keywords


EID: 85065510872     PISSN: None     EISSN: 23670126     Source Type: Journal    
DOI: 10.1186/s41546-016-0008-x     Document Type: Article
Times cited : (65)

References (40)
  • 1
    • 75849149693 scopus 로고    scopus 로고
    • Optimal execution strategies in limit order books with general shape functions
    • Alfonsi, A, Fruth, A, Schied, A: Optimal execution strategies in limit order books with general shape functions. Quantit. Finance 10, 143–157 (2010)
    • (2010) Quantit. Finance , vol.10 , pp. 143-157
    • Alfonsi, A1    Fruth, A2    Schied, A3
  • 2
    • 0344354031 scopus 로고    scopus 로고
    • Optimal execution of portfolio transactions
    • Almgren, R, Chriss, N: Optimal execution of portfolio transactions. J. Risk 3, 5–39 (2000)
    • (2000) J. Risk , vol.3 , pp. 5-39
    • Almgren, R1    Chriss, N2
  • 4
    • 79958262462 scopus 로고    scopus 로고
    • A maximum principle for SDEs of mean-field type
    • Andersson, D, Djehiche, B: A maximum principle for SDEs of mean-field type. Appl. Math. Optimization 63, 341–356 (2010)
    • (2010) Appl. Math. Optimization , vol.63 , pp. 341-356
    • Andersson, D1    Djehiche, B2
  • 6
    • 84990847952 scopus 로고    scopus 로고
    • Hedging with transient price impact
    • arXiv: 1510.03223v1, to appear in
    • Bank, P, Soner, M, Voss, M: Hedging with transient price impact. arXiv: 1510.03223v1, to appear in Mathematics and Financial Economics (2015). http://link.springer.com/article/10.1007/s11579-016-0178-4
    • (2015) Mathematics and Financial Economics
    • Bank, P1    Soner, M2    Voss, M3
  • 7
    • 77954963823 scopus 로고    scopus 로고
    • Dynamic mean-variance asset allocation
    • Basak, S, Chabakauri, G: Dynamic mean-variance asset allocation. Rev. Finan. Stud 23, 2970–3016 (2010)
    • (2010) Rev. Finan. Stud , vol.23 , pp. 2970-3016
    • Basak, S1    Chabakauri, G2
  • 9
    • 0016949806 scopus 로고
    • Linear quadratic optimal stochastic control with random coefficients
    • Bismut, JM: Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim 14, 419–444 (1976)
    • (1976) SIAM J. Control Optim , vol.14 , pp. 419-444
    • Bismut, JM1
  • 10
    • 77955647213 scopus 로고    scopus 로고
    • McKean-Vlasov limit in portfolio optimization
    • Borkar, V, Kumar, KS: McKean-Vlasov limit in portfolio optimization. Stoch. Anal. Appl. 28, 884–906 (2010)
    • (2010) Stoch. Anal. Appl , vol.28 , pp. 884-906
    • Borkar, V1    Kumar, KS2
  • 11
    • 80052971337 scopus 로고    scopus 로고
    • A general maximum principle for SDEs of mean-field type
    • Buckdahn, R, Djehiche, B, Li, J: A general maximum principle for SDEs of mean-field type. Appl. Math. Optim 64(2), 197–216 (2011)
    • (2011) Appl. Math. Optim , vol.64 , Issue.2 , pp. 197-216
    • Buckdahn, R1    Djehiche, B2    Li, J3
  • 16
    • 84947717362 scopus 로고    scopus 로고
    • Forward-backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics
    • Carmona, R, Delarue, F: Forward-backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics. Ann. Probab 43(5), 2647–2700 (2015)
    • (2015) Ann. Probab , vol.43 , Issue.5 , pp. 2647-2700
    • Carmona, R1    Delarue, F2
  • 17
    • 84979084054 scopus 로고    scopus 로고
    • A probabilistic approach to mean field games with major and minor players
    • arXiv: 1409.7141v1
    • Carmona, R, Zhu, X: A probabilistic approach to mean field games with major and minor players. Ann. Appl. Prob 26(3), 1535–1580 (2016). arXiv: 1409.7141v1
    • (2016) Ann. Appl. Prob , vol.26 , Issue.3 , pp. 1535-1580
    • Carmona, R1    Zhu, X2
  • 18
    • 84876129326 scopus 로고    scopus 로고
    • Control of McKean-Vlasov dynamics versus mean field games
    • Carmona, R, Delarue, F, Lachapelle, A: Control of McKean-Vlasov dynamics versus mean field games. Math. Financial Econ 7, 131–166 (2013)
    • (2013) Math. Financial Econ , vol.7 , pp. 131-166
    • Carmona, R1    Delarue, F2    Lachapelle, A3
  • 19
    • 84930019381 scopus 로고    scopus 로고
    • Mean field games and systemic risk. to appear in Communications in Mathematical Sciences
    • Carmona, R, Fouque, JP, Sun, LH: Mean field games and systemic risk. to appear in Communications in Mathematical Sciences. Communications in Mathematical Sciences 13(4), 911-933 (2015)
    • (2015) Communications in Mathematical Sciences , vol.13 , Issue.4 , pp. 911-933
    • Carmona, R1    Fouque, JP2    Sun, LH3
  • 20
    • 85132441337 scopus 로고    scopus 로고
    • A closed-form execution strategy to target VWAP
    • to appear in Preprint
    • Cartea, A, Jaimungal, S: A closed-form execution strategy to target VWAP. to appear in SIAM Journal of Financial Mathematics (2015). Preprint available at https://papers.ssrn.com/sol3/papers.cfm?abstract id=2542314
    • (2015) SIAM Journal of Financial Mathematics
    • Cartea, A1    Jaimungal, S2
  • 22
    • 0001866003 scopus 로고
    • Les aspects probabilistes du contrôle stochastique. Ninth Saint Flour Probability Summer School-1979
    • Springer
    • El Karoui, N: Les aspects probabilistes du contrôle stochastique. Ninth Saint Flour Probability Summer School-1979. Lecture Notes Math 876, 73–238 (1981), Springer
    • (1981) Lecture Notes Math , vol.876 , pp. 73-238
    • El Karoui, N1
  • 23
    • 84930376419 scopus 로고    scopus 로고
    • Optimal execution of a VWAP order: a stochastic control approach
    • Frei, C, Westray, N: Optimal execution of a VWAP order: a stochastic control approach. Math. Finance 25, 612–639 (2015)
    • (2015) Math. Finance , vol.25 , pp. 612-639
    • Frei, C1    Westray, N2
  • 24
    • 84865529161 scopus 로고    scopus 로고
    • Time-inconsistent stochastic linear-quadratic control
    • Hu, Y, Jin, H, Zhou, XY: Time-inconsistent stochastic linear-quadratic control. SIAM J. Control Optim 50, 1548–1572 (2012)
    • (2012) SIAM J. Control Optim , vol.50 , pp. 1548-1572
    • Hu, Y1    Jin, H2    Zhou, XY3
  • 25
    • 84921765673 scopus 로고    scopus 로고
    • A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon
    • Huang, J, Li, X, Yong, J: A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon. Math. Control Related Fields 5, 97–139 (2015)
    • (2015) Math. Control Related Fields , vol.5 , pp. 97-139
    • Huang, J1    Li, X2    Yong, J3
  • 27
    • 0033722043 scopus 로고    scopus 로고
    • Continuous-time mean-variance portfolio selection: a stochastic LQ framework
    • Li, D, Zhou, XY: Continuous-time mean-variance portfolio selection: a stochastic LQ framework. Appl. Math. Optim 42, 19–33 (2000)
    • (2000) Appl. Math. Optim , vol.42 , pp. 19-33
    • Li, D1    Zhou, XY2
  • 30
    • 0026834859 scopus 로고
    • Stochastic Hamilton Jacobi Bellman equations
    • Peng, S: Stochastic Hamilton Jacobi Bellman equations. SIAM J. Control Optim 30, 284–304 (1992)
    • (1992) SIAM J. Control Optim , vol.30 , pp. 284-304
    • Peng, S1
  • 33
    • 84868245353 scopus 로고    scopus 로고
    • Optimal execution in a general one-sided limit-order book
    • Predoiu, S, Shaikhet, G, Shreve, S: Optimal execution in a general one-sided limit-order book. SIAM J. Financial Math 2, 183–212 (2011)
    • (2011) SIAM J. Financial Math , vol.2 , pp. 183-212
    • Predoiu, S1    Shaikhet, G2    Shreve, S3
  • 34
    • 77957118884 scopus 로고    scopus 로고
    • The cost of illiquidity and its effects on hedging
    • Rogers, LCG, Singh, S: The cost of illiquidity and its effects on hedging. Mathematical Finance 20, 597–615 (2010)
    • (2010) Mathematical Finance , vol.20 , pp. 597-615
    • Rogers, LCG1    Singh, S2
  • 36
    • 84920200956 scopus 로고    scopus 로고
    • Linear Quadratic Stochastic Differential Games: Open-Loop and Closed-Loop Saddle Points
    • Sun, J, Yong, J: Linear Quadratic Stochastic Differential Games: Open-Loop and Closed-Loop Saddle Points. SIAM J. Control Optim 52, 4082–4121 (2014)
    • (2014) SIAM J. Control Optim , vol.52 , pp. 4082-4121
    • Sun, J1    Yong, J2
  • 37
    • 1842532397 scopus 로고    scopus 로고
    • General linear quadratic optimal stochastic control problems with random coefficients: linear stochastic Hamilton systems and backward stochastic Riccati equations
    • Tang, S: General linear quadratic optimal stochastic control problems with random coefficients: linear stochastic Hamilton systems and backward stochastic Riccati equations. SIAM J. Control Optim 42, 53–75 (2003)
    • (2003) SIAM J. Control Optim , vol.42 , pp. 53-75
    • Tang, S1
  • 38
    • 0001042840 scopus 로고
    • On a matrix Riccati equation of stochastic control
    • Wonham, W: On a matrix Riccati equation of stochastic control. SIAM J. Control 6, 681–697 (1968)
    • (1968) SIAM J. Control , vol.6 , pp. 681-697
    • Wonham, W1
  • 39
    • 84885675349 scopus 로고    scopus 로고
    • A linear-quadratic optimal control problem for mean-field stochastic differential equations
    • Yong, J: A linear-quadratic optimal control problem for mean-field stochastic differential equations. SIAM J. Control Optim 51(4), 2809–2838 (2013)
    • (2013) SIAM J. Control Optim , vol.51 , Issue.4 , pp. 2809-2838
    • Yong, J1


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