Space-distribution PDEs for path independent additive functionals of McKean-Vlasov SDEs

被引:16
作者
Ren, Panpan [1 ]
Wang, Feng-Yu [1 ,2 ]
机构
[1] Swansea Univ, Dept Math, Singleton Pk, Swansea SA2 8PP, W Glam, Wales
[2] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China
关键词
McKean-Vlasov SDEs; additive functional; Girsanov transformation; L-derivative; STOCHASTIC DIFFERENTIAL-EQUATIONS; GIRSANOV TRANSFORMATION; MEAN-FIELD;
D O I
10.1142/S0219025720500186
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let 2(d) be the space of probability measures on d with finite second moment. The path independence of additive functionals of McKean-Vlasov SDEs is characterized by PDEs on the product space d x 2(d) equipped with the usual derivative in space variable and Lions' derivative in distribution. These PDEs are solved by using probabilistic arguments developed from Ref. 2. As a consequence, the path independence of Girsanov transformations is identified with nonlinear PDEs on d x 2(d) whose solutions are given by probabilistic arguments as well. In particular, the corresponding results on the Girsanov transformation killing the drift term derived earlier for the classical SDEs are recovered as special situations.
引用
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页数:15
相关论文
共 17 条
[1]   PRICING OF OPTIONS AND CORPORATE LIABILITIES [J].
BLACK, F ;
SCHOLES, M .
JOURNAL OF POLITICAL ECONOMY, 1973, 81 (03) :637-654
[2]   MEAN-FIELD STOCHASTIC DIFFERENTIAL EQUATIONS AND ASSOCIATED PDES [J].
Buckdahn, Rainer ;
Li, Juan ;
Peng, Shige ;
Rainer, Catherine .
ANNALS OF PROBABILITY, 2017, 45 (02) :824-878
[3]  
Cardaliaguet P., P L LIONS LECT COLL
[4]  
Chassagneux JF, 2014, PREPRINT
[5]  
HAMMERSLEY W, 2018, PREPRINT
[6]   QUASI-MEAN REVERSION IN AN EFFICIENT STOCK-MARKET - THE CHARACTERIZATION OF ECONOMIC EQUILIBRIA WHICH SUPPORT BLACK SCHOLES OPTION PRICING [J].
HODGES, S ;
CARVERHILL, A .
ECONOMIC JOURNAL, 1993, 103 (417) :395-405
[7]  
Huang X.-L., 2018, PREPRINT
[8]   Mean-field forward and backward SDEs with jumps and associated nonlocal quasi-linear integral-PDEs [J].
Li, Juan .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2018, 128 (09) :3118-3180
[9]  
Mishura Yu. S., 2016, PREPRINT
[10]   Characterizing the path-independence of the Girsanov transformation for non-Lipschitz SDEs with jumps [J].
Qiao, Huijie ;
Wu, Jiang-Lun .
STATISTICS & PROBABILITY LETTERS, 2016, 119 :326-333