메뉴 건너뛰기




Volumn 27, Issue 5, 2017, Pages 2698-2752

A stochastic mckean-vlasov equation for absorbing diffusions on the half-line

Author keywords

McKean Vlasov problem; Nonlinear SPDE; Skorokhod M1 topology

Indexed keywords


EID: 85033681561     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/16-AAP1256     Document Type: Article
Times cited : (32)

References (55)
  • 1
    • 85033706767 scopus 로고    scopus 로고
    • A stochastic partial differential equation model for mortgage backed securities
    • AHMAD, F., HAMBLY, B. M. A nd LEDGER, S. (2016). A stochastic partial differential equation model for mortgage backed securities. Preprint.
    • (2016) Preprint
    • Ahmad, F.1    Hambly, B.M.2    Ledger, S.3
  • 2
    • 33746629616 scopus 로고    scopus 로고
    • Extensions to the Gaussian copula: Random recovery and random factor loadings
    • ANDERSEN, L. A nd SIDENIUS, J. (2005). Extensions to the Gaussian copula: Random recovery and random factor loadings. J. Credit Risk 1 29-70.
    • (2005) J. Credit Risk , vol.1 , pp. 29-70
    • Andersen, L.1    Sidenius, J.2
  • 4
    • 85033721097 scopus 로고    scopus 로고
    • Convergence of probability measures, 2nd ed
    • BILLINGSLEY, P. (1999). Convergence of Probability Measures, 2nd ed. Wiley, New York.
    • (1999) Wiley, New York
    • Billingsley, P.1
  • 5
    • 84944831925 scopus 로고
    • Valuing corporate securities: Some effects of bond indenture provisions
    • BLACK, F. A nd COX, J. (1976). Valuing corporate securities: Some effects of bond indenture provisions. J. Finance 31 351-367.
    • (1976) J. Finance , vol.31 , pp. 351-367
    • Black, F.1    Cox, J.2
  • 6
    • 84973662788 scopus 로고    scopus 로고
    • Numerical valuation of basket credit derivatives in structural jump-diffusion models
    • BUJOK, K. A nd REISINGER, C. (2012). Numerical valuation of basket credit derivatives in structural jump-diffusion models. J. Comput. Finance 15 115-158.
    • (2012) J. Comput. Finance , vol.15 , pp. 115-158
    • Bujok, K.1    Reisinger, C.2
  • 7
    • 43849087039 scopus 로고    scopus 로고
    • Beyond the Gaussian copula: Stochastic and local correlation
    • BURTSCHELL, X., GREGORY, J. A nd LAURENT, J.-P. (2007). Beyond the Gaussian copula: Stochastic and local correlation. J. Credit Risk 3 31-62.
    • (2007) J. Credit Risk , vol.3 , pp. 31-62
    • Burtschell, X.1    Gregory, J.2    Laurent, J.-P.3
  • 9
    • 84861627504 scopus 로고    scopus 로고
    • Analysis of nonlinear noisy integrate & fire neuron models: Blow-up and steady states
    • MR2853216
    • CÁCERES, M. J., CARRILLO, J. A . A nd PERTHAME, B. (2011). A nalysis of nonlinear noisy integrate & fire neuron models: Blow-up and steady states. J. Math. Neurosci. 1 Art. 7, 33. MR2853216
    • (2011) J. Math. Neurosci. , vol.1 , pp. 33
    • Cáceres, M.J.1    Carrillo, J.A.2    Perthame, B.3
  • 10
    • 84881309217 scopus 로고    scopus 로고
    • Probabilistic analysis of mean-field games
    • CARMONA, R. A nd DELARUE, F. (2013). Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51 2705-2734.
    • (2013) SIAM J. Control Optim. , vol.51 , pp. 2705-2734
    • Carmona, R.1    Delarue, F.2
  • 14
    • 84879079623 scopus 로고
    • Mckean-vlasov equations with discontinuous coefficients
    • MR1309485
    • CHIANG, T. S. (1994). McKean-Vlasov equations with discontinuous coefficients. Soochow J. Math. 20 507-526. MR1309485
    • (1994) Soochow J. Math. , vol.20 , pp. 507-526
    • Chiang, T.S.1
  • 15
    • 84903595658 scopus 로고    scopus 로고
    • Conditional distributions, exchangeable particle systems, and stochastic partial differential equations
    • MR3224295
    • CRISAN, D., KURTZ, T. G. A nd LEE, Y. (2014). Conditional distributions, exchangeable particle systems, and stochastic partial differential equations. A nn. Inst. Henri Poincaré Probab. Stat. 50 946-974. MR3224295
    • (2014) Ann. Inst. Henri Poincaré Probab. Stat. , vol.50 , pp. 946-974
    • Crisan, D.1    Kurtz, T.G.2    Lee, Y.3
  • 16
    • 76849109369 scopus 로고    scopus 로고
    • Approximate mckean-vlasov representations for a class of spdes
    • CRISAN, D. A nd XIONG, J. (2010). A pproximate McKean-Vlasov representations for a class of SPDEs. Stochastics 82 1-16.
    • (2010) Stochastics , vol.82 , pp. 1-16
    • Crisan, D.1    Xiong, J.2
  • 18
    • 85033722865 scopus 로고    scopus 로고
    • Spatial fleming-viot models with selection and mutation
    • DAWSON, D. A nd GREVEN, A. (2014). Spatial Fleming-Viot Models with Selection and Mutation. Springer, Berlin.
    • (2014) Springer, Berlin
    • Dawson, D.1    Greven, A.2
  • 19
    • 84936791750 scopus 로고    scopus 로고
    • Global solvability of a networked integrate-and-fire model of mckean-vlasov type
    • MR3349003
    • DELARUE, F., INGLIS, J., RUBENTHALER, S. A nd TANRÉ, E. (2015). Global solvability of a networked integrate-and-fire model of McKean-Vlasov type. A nn. A ppl. Probab. 25 2096-2133. MR3349003
    • (2015) Ann. A ppl. Probab. , vol.25 , pp. 2096-2133
    • Delarue, F.1    Inglis, J.2    Rubenthaler, S.3    Tanré, E.4
  • 21
  • 22
    • 69949097519 scopus 로고    scopus 로고
    • Time-changed birth processes and multiname credit derivatives
    • DING, X., GIESECKE, K. A nd TOMECEK, P. (2009). Time-changed birth processes and multiname credit derivatives. Oper. Res. 57 990-1005.
    • (2009) Oper. Res. , vol.57 , pp. 990-1005
    • Ding, X.1    Giesecke, K.2    Tomecek, P.3
  • 25
    • 84880281017 scopus 로고    scopus 로고
    • Fast valuation and calibration of credit default swaps under lévy processes
    • FANG, F., JÖNSSON, H., OOSTERLEE, C. A nd SCHOUTENS, W. (2010). Fast valuation and calibration of credit default swaps under Lévy processes. J. Comput. Finance 14 1-30.
    • (2010) J. Comput. Finance , vol.14 , pp. 1-30
    • Fang, F.1    Jönsson, H.2    Oosterlee, C.3    Schoutens, W.4
  • 26
    • 77956333748 scopus 로고    scopus 로고
    • Issues in the pricing of synthetic cdos
    • FINGER, C. C. (2005). Issues in the pricing of synthetic CDOs. J. Credit Risk 1 113-124.
    • (2005) J. Credit Risk , vol.1 , pp. 113-124
    • Finger, C.C.1
  • 27
    • 4043160769 scopus 로고    scopus 로고
    • Dependent defaults in modes of portfolio credit risk
    • FREY, R. A ndMCNEIL, A. (2003). Dependent defaults in modes of portfolio credit risk. J. Risk 6 59-92.
    • (2003) J. Risk , vol.6 , pp. 59-92
    • Frey, R.1    McNeil, A.2
  • 29
    • 33645955582 scopus 로고    scopus 로고
    • Credit contagion and aggregate losses
    • MR2224986
    • GIESECKE, K. A nd WEBER, S. (2006). Credit contagion and aggregate losses. J. Econom. Dynam. Control 30 741-767. MR2224986
    • (2006) J. Econom. Dynam. Control , vol.30 , pp. 741-767
    • Giesecke, K.1    Weber, S.2
  • 30
    • 84870887091 scopus 로고    scopus 로고
    • Stochastic finite differences and multilevel monte carlo for a class of spdes in finance
    • GILES, M. A nd REISINGER, C. (2012). Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance. SIAM J. Financial Math. 3 572-592.
    • (2012) SIAM J. Financial Math. , vol.3 , pp. 572-592
    • Giles, M.1    Reisinger, C.2
  • 31
    • 85007431261 scopus 로고    scopus 로고
    • Valuing credit default swaps II: Modeling default correlations
    • HULL, J. A nd WHITE, A. (2001). Valuing credit default swaps II: Modeling default correlations. J. Derivatives 8 12-21.
    • (2001) J. Derivatives , vol.8 , pp. 12-21
    • Hull, J.1    White, A.2
  • 34
    • 84884576147 scopus 로고    scopus 로고
    • A sobolev space theory for parabolic stochastic pdes driven by lévy processes on c1-domains
    • MR3131301
    • KIM, K.-H. (2014). A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on C1-domains. Stochastic Process. A ppl. 124 440-474. MR3131301
    • (2014) Stochastic Process. A ppl. , vol.124 , pp. 440-474
    • Kim, K.-H.1
  • 35
    • 84880197132 scopus 로고    scopus 로고
    • Nonlinear diffusions and stable-like processes with coefficients depending on the median or var
    • MR3072241
    • KOLOKOLTSOV, V. N. (2013). Nonlinear diffusions and stable-like processes with coefficients depending on the median or VaR. A ppl. Math. Optim. 68 85-98. MR3072241
    • (2013) Appl. Math. Optim. , vol.68 , pp. 85-98
    • Kolokoltsov, V.N.1
  • 37
    • 21844514446 scopus 로고
    • A class of quasilinear stochastic partial differential equations of mckean-vlasov type with mass conservation
    • KOTELENEZ, P. (1995). A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation. Probab. Theory Related Fields 102 159-188.
    • (1995) Probab. Theory Related Fields , vol.102 , pp. 159-188
    • Kotelenez, P.1
  • 38
    • 0000273833 scopus 로고    scopus 로고
    • Particle representations for a class of nonlinear spdes
    • KURTZ, T. G. A nd XIONG, J. (1999). Particle representations for a class of nonlinear SPDEs. Stochastic Process. A ppl. 83 103-126.
    • (1999) Stochastic Process. A ppl. , vol.83 , pp. 103-126
    • Kurtz, T.G.1    Xiong, J.2
  • 39
    • 85033678326 scopus 로고    scopus 로고
    • Sharp regularity near an absorbing boundary for solutions to second order spdes in a half-line with constant coefficients
    • MR3249578
    • LEDGER, S. (2014). Sharp regularity near an absorbing boundary for solutions to second order SPDEs in a half-line with constant coefficients. Stoch. Partial Differ. Equ. A nal. Computat. 2 1-26. MR3249578
    • (2014) Stoch. Partial Differ. Equ. A nal. Computat. , vol.2 , pp. 1-26
    • Ledger, S.1
  • 40
    • 84965042590 scopus 로고    scopus 로고
    • Skorokhod's m1 topology for distribution-valued processes
    • MR3492929
    • LEDGER, S. (2016). Skorokhod's M1 topology for distribution-valued processes. Electron. Commun. Probab. 21 Paper No. 34, 11. MR3492929
    • (2016) Electron. Commun. Probab. 21 Paper No. 34 , vol.11
    • Ledger, S.1
  • 41
    • 85011528625 scopus 로고    scopus 로고
    • Common poisson shock models: Applications to insurance and credit risk modelling
    • LINDSKOG, F. A ndMCNIEL, A. (2003). Common Poisson shock models: Applications to insurance and credit risk modelling. A stin Bull. 33 209-238.
    • (2003) Astin Bull. , vol.33 , pp. 209-238
    • Lindskog, F.1    McNiel, A.2
  • 42
    • 84898909005 scopus 로고    scopus 로고
    • Mean field limit for disordered diffusions with singular interactions
    • MR3226169
    • LUÇON, E. A nd STANNAT, W. (2014). Mean field limit for disordered diffusions with singular interactions. A nn. A ppl. Probab. 24 1946-1993. MR3226169
    • (2014) Ann. A ppl. Probab. , vol.24 , pp. 1946-1993
    • Luçon, E.1    Stannat, W.2
  • 43
    • 11144348575 scopus 로고    scopus 로고
    • Calculating portfolio loss
    • MERINO, S. A nd NYFELER, M. A . (2002). Calculating portfolio loss. RISK 82-86.
    • (2002) RISK , pp. 82-86
    • Merino, S.1    Nyfeler, M.A.2
  • 44
    • 0000808665 scopus 로고
    • On the pricing of corporate debt: The risk structure of interest rates
    • MERTON, R. (1974). On the pricing of corporate debt: The risk structure of interest rates. J. Finance 29 449-470.
    • (1974) J. Finance , vol.29 , pp. 449-470
    • Merton, R.1
  • 45
    • 34547261198 scopus 로고    scopus 로고
    • Semi-analytical valuation of basket credit derivatives in intensitybased models
    • MORTENSEN, A. (2006). Semi-analytical valuation of basket credit derivatives in intensitybased models. J. Derivatives 13 8-26.
    • (2006) J. Derivatives , vol.13 , pp. 8-26
    • Mortensen, A.1
  • 47
    • 84966247213 scopus 로고
    • Real and complex analysis, 3rd ed
    • MR0924157
    • RUDIN, W. (1987). Real and Complex Analysis, 3rd ed. McGraw-Hill, New York. MR0924157
    • (1987) McGraw-Hill, New York
    • Rudin, W.1
  • 48
    • 85033664049 scopus 로고    scopus 로고
    • Credit derivatives pricing models: Models, pricing and implementation
    • SCHÖNBUCHER, P. J. (2003). Credit Derivatives Pricing Models: Models, Pricing and Implementation. Wiley, New York.
    • (2003) Wiley, New York
    • Schönbucher, P.J.1
  • 50
    • 0001105004 scopus 로고
    • Topics in propagation of chaos
    • P.-L. Hennequin, ed.). Lecture Notes in Mathematics, Chapter 3, . Springer, Berlin
    • SZNITMAN, A.-S. (1991). Topics in propagation of chaos. In Ecole D'Eté de Probabilités de Saint-Flour XIX-1989 (P.-L. Hennequin, ed.). Lecture Notes in Mathematics, Chapter 3, 1464 165-251. Springer, Berlin.
    • (1991) Ecole D'Eté de Probabilités de Saint-Flour XIX-1989 , vol.1464 , pp. 165-251
    • Sznitman, A.-S.1
  • 52
    • 84865203826 scopus 로고    scopus 로고
    • The stochastic fubini theorem revisited
    • MR2966093
    • VERAAR, M. (2012). The stochastic Fubini theorem revisited. Stochastics 84 543-551. MR2966093
    • (2012) Stochastics , vol.84 , pp. 543-551
    • Veraar, M.1
  • 54
    • 84870542411 scopus 로고    scopus 로고
    • Valuation of synthetic cdos with affine jump-diffusion processes involving lévy stable distributions
    • MR3011182
    • WU, J.-L. A nd YANG, W. (2013). Valuation of synthetic CDOs with affine jump-diffusion processes involving Lévy stable distributions. Math. Comput. Modelling 57 570-583. MR3011182
    • (2013) Math. Comput. Modelling , vol.57 , pp. 570-583
    • Wu, J.-L.1    Yang, W.2
  • 55
    • 0035614682 scopus 로고    scopus 로고
    • An analysis of default correlations and multiple defaults
    • ZHOU, C. (2001). A n analysis of default correlations and multiple defaults. Rev. Financ. Stud. 14 555-576.
    • (2001) Rev. Financ. Stud. , vol.14 , pp. 555-576
    • Zhou, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.