메뉴 건너뛰기




Volumn 21, Issue 2, 2011, Pages 397-463

Affine processes on positive semidefinite matrices

Author keywords

Affine processes; Stochastic invariance; Stochastic volatility; Wishart processes

Indexed keywords


EID: 79953292816     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/10-AAP710     Document Type: Article
Times cited : (140)

References (52)
  • 1
    • 0003226050 scopus 로고
    • Functional equations in several variables
    • Cambridge Univ. Press, Cambridge. MR1004465
    • ACZÉL, J. and DHOMBRES, J. (1989). Functional Equations in Several Variables. Encyclopedia of Mathematics and Its Applications 31. Cambridge Univ. Press, Cambridge. MR1004465
    • (1989) Encyclopedia of Mathematics and its Applications , vol.31
    • Aczél, J.1    Dhombres, J.2
  • 3
    • 72549104240 scopus 로고    scopus 로고
    • Positive-definite matrix processes of finite variation
    • MR2353270
    • BARNDORFF-NIELSEN, O. E. and STELZER, R. (2007). Positive-definite matrix processes of finite variation. Probab. Math. Statist. 27 3-43. MR2353270
    • (2007) Probab. Math. Statist. , vol.27 , pp. 3-43
    • Barndorff-Nielsen, O.E.1    Stelzer, R.2
  • 5
    • 38249023663 scopus 로고
    • Diffusions of perturbed principal component analysis
    • MR0991060
    • BRU, M.-F. (1989). Diffusions of perturbed principal component analysis. J. Multivariate Anal. 29 127-136. MR0991060
    • (1989) J. Multivariate Anal , vol.29 , pp. 127-136
    • Bru, M.-F.1
  • 6
    • 3042671100 scopus 로고
    • Wishart processes
    • MR1132135
    • BRU, M.-F. (1991). Wishart processes. J. Theoret. Probab. 4 725-751. MR1132135
    • (1991) J. Theoret. Probab. , vol.4 , pp. 725-751
    • Bru, M.-F.1
  • 7
    • 53849113472 scopus 로고    scopus 로고
    • Correlation risk and the term structure of interest rates
    • Univ. St. Gallen.
    • BURASCHI, B., CIESLAK, A. and TROJANI, F. (2007). Correlation risk and the term structure of interest rates. Working paper, Univ. St. Gallen.
    • (2007) Working paper
    • Buraschi, B.1    Cieslak, A.2    Trojani, F.3
  • 8
    • 74249123832 scopus 로고    scopus 로고
    • Correlation risk and optimal portfolio choice
    • BURASCHI, B., PORCHIA, P. and TROJANI, F. (2010). Correlation risk and optimal portfolio choice. J. Finance 65 393-420.
    • (2010) J. Finance , vol.65 , pp. 393-420
    • Buraschi, B.1    Porchia, P.2    Trojani, F.3
  • 9
    • 79953273810 scopus 로고    scopus 로고
    • Hedging (co)variance risk with variance swaps
    • ESILV RR-37 Ecole Supérieure d'Ingénierie Léonard de Vinci
    • DA FONSECA, J., GRASSELLI, M. and IELPO, F. (2008). Hedging (co)variance risk with variance swaps. Working paper ESILV RR-37, Ecole Supérieure d'Ingénierie Léonard de Vinci.
    • (2008) Working paper
    • Da Fonseca, J.1    Grasselli, M.2    Ielpo, F.3
  • 10
    • 79953268060 scopus 로고    scopus 로고
    • Estimating the Wishart affine stochastic correlation model using the empirical characteristic function
    • ESILV RR-35, Ecole Supérieure d'Ingénierie Léonard de Vinci.
    • DA FONSECA, J., GRASSELLI, M. and IELPO, F. (2008). Estimating the Wishart affine stochastic correlation model using the empirical characteristic function. Working paper ESILV RR-35, Ecole Supérieure d'Ingénierie Léonard de Vinci.
    • (2008) Working paper
    • Da Fonseca, J.1    Grasselli, M.2    Ielpo, F.3
  • 11
    • 41249095007 scopus 로고    scopus 로고
    • Option pricing when correlations are stochastic: An analytical framework
    • DA FONSECA, J.,GRASSELLI, M. and TEBALDI, C. (2007). Option pricing when correlations are stochastic: An analytical framework. Review of Derivatives Research 10 151-180.
    • (2007) Review of Derivatives Research , vol.10 , pp. 151-180
    • Da Fonseca1    J.Grasselli, M.2    Tebaldi, C.3
  • 12
    • 52149109890 scopus 로고    scopus 로고
    • A multifactor volatility heston model
    • MR2457710
    • DA FONSECA, J., GRASSELLI, M. and TEBALDI, C. (2008). A multifactor volatility Heston model. Quant. Finance 8 591-604. MR2457710
    • (2008) Quant. Finance , vol.8 , pp. 591-604
    • Da Fonseca, J.1    Grasselli, M.2    Tebaldi, C.3
  • 13
    • 2342649571 scopus 로고    scopus 로고
    • Invariance of stochastic control systems with deterministic arguments
    • DOI 10.1016/j.jde.2004.01.007
    • DA PRATO, G. and FRANKOWSKA, H. (2004). Invariance of stochastic control systems with deterministic arguments. J. Differential Equations 200 18-52. MR2046316 (Pubitemid 38582651)
    • (2004) Journal of Differential Equations , vol.200 , Issue.1 , pp. 18-52
    • Da Prato, G.1    Frankowska, H.2
  • 18
    • 14844348230 scopus 로고    scopus 로고
    • Time-inhomogeneous affine processes
    • DOI 10.1016/j.spa.2004.11.006, PII S0304414904001838
    • FILIPOVIĆ, D. (2005). Time-inhomogeneous affine processes. Stochastic Process. Appl. 115 639-659. MR2128634 (Pubitemid 40351936)
    • (2005) Stochastic Processes and their Applications , vol.115 , Issue.4 , pp. 639-659
    • Filipovic, D.1
  • 20
    • 71249118865 scopus 로고    scopus 로고
    • Affine diffusion processes: Theory and applications. In advanced financial modelling
    • Walter de Gruyter, Berlin. MR2648460
    • FILIPOVÍC, D. and MAYERHOFER, E. (2009). Affine diffusion processes: Theory and applications. In Advanced Financial Modelling. Radon Ser. Comput. Appl. Math. 8 125-164. Walter de Gruyter, Berlin. MR2648460
    • (2009) Radon Ser. Comput. Appl. Math. , vol.8 , pp. 125-164
    • Filipović, D.1    Mayerhofer, E.2
  • 22
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed. Johns Hopkins Univ. Press, Baltimore, MD. MR1417720
    • GOLUB, G. H. and VAN LOAN, C. F. (1996). Matrix Computations, 3rd ed. Johns Hopkins Univ. Press, Baltimore, MD. MR1417720
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 23
    • 79953278452 scopus 로고    scopus 로고
    • International money and stock market contingent claims
    • CREST, CEPREMAP and Univ. Toronto
    • GOURIEROUX, C., MONTFORT, A. and SUFANA, R. (2007). International money and stock market contingent claims. Working paper, CREST, CEPREMAP and Univ. Toronto.
    • (2007) Working Paper
    • Gourieroux, C.1    Montfort, A.2    Sufana, R.3
  • 24
    • 79960130734 scopus 로고    scopus 로고
    • Wishart quadratic term structure models
    • CREST, CEPREMAP and Univ. Toronto
    • GOURIEROUX, C. and SUFANA, R. (2007).Wishart quadratic term structure models.Working paper, CREST, CEPREMAP and Univ. Toronto.
    • (2007) Working Paper
    • Gourieroux, C.1    Sufana, R.2
  • 25
    • 33747790964 scopus 로고    scopus 로고
    • Derivative pricing with Wishart multivariate stochastic volatility: Application to credit risk
    • CREST, CEPREMAP and Univ. Toronto
    • GOURIEROUX, C. and SUFANA, R. (2007). Derivative pricing with Wishart multivariate stochastic volatility: Application to credit risk. Working paper, CREST, CEPREMAP and Univ. Toronto.
    • (2007) Working paper
    • Gourieroux, C.1    Sufana, R.2
  • 26
    • 37249024189 scopus 로고    scopus 로고
    • Solvable affine term structure models
    • MR2380943
    • GRASSELLI, M. and TEBALDI, C. (2008). Solvable affine term structure models. Math. Finance 18 135-153. MR2380943
    • (2008) Math. Finance , vol.18 , pp. 135-153
    • Grasselli, M.1    Tebaldi, C.2
  • 27
    • 0037836721 scopus 로고
    • A closed-form solution for options with stochastic volatility with applications to bond and currency options
    • HESTON, S. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. of Financial Studies 6 327-343.
    • (1993) Rev. of Financial Studies , vol.6 , pp. 327-343
    • Heston, S.1
  • 28
    • 0003529551 scopus 로고
    • Grundlehren der MathematischenWissenschaften [Fundamental Principles of Mathematical Sciences], Springer, Berlin. MR1261420
    • HIRIART-URRUTY, J.-B. and LEMARÉCHAL, C. (1993). Convex Analysis and Minimization Algorithms. I. Grundlehren der MathematischenWissenschaften [Fundamental Principles of Mathematical Sciences] 305. Springer, Berlin. MR1261420
    • (1993) Convex Analysis and Minimization Algorithms , vol.1 , pp. 305
    • Hiriart-Urruty, J.-B.1    LemaréChal, C.2
  • 30
    • 0000531113 scopus 로고
    • Multivariate point processes: Predictable projection, radon-nikodým derivatives, representation of martingales
    • MR0380978
    • JACOD, J. (1974/75). Multivariate point processes: Predictable projection, Radon-Nikodým derivatives, representation of martingales. Z. Wahrsch. Verw. Gebiete 31 235-253. MR0380978
    • (1974) Z. Wahrsch. Verw. Gebiete , vol.31 , pp. 235-253
    • Jacod, J.1
  • 31
    • 0003757289 scopus 로고    scopus 로고
    • 2nd ed. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer, Berlin. MR1943877
    • JACOD, J. and SHIRYAEV, A. N. (2003). Limit Theorems for Stochastic Processes, 2nd ed. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 288. Springer, Berlin. MR1943877
    • (2003) Limit Theorems for Stochastic Processes , vol.288
    • Jacod, J.1    Shiryaev, A.N.2
  • 34
    • 77953675918 scopus 로고    scopus 로고
    • Affine processes-theory and applications in mathematical finance
    • Ph.D. thesis, Vienna Univ
    • KELLER-RESSEL, M. (2009). Affine processes-theory and applications in mathematical finance. Ph.D. thesis, Vienna Univ. Technology.
    • (2009) Technology
    • Keller-Ressel, M.1
  • 37
    • 0004480637 scopus 로고
    • Real and functional analysis
    • 3rd ed, Springer, New York. MR1216137
    • LANG, S. (1993). Real and Functional Analysis, 3rd ed. Graduate Texts in Mathematics 142. Springer, New York. MR1216137
    • (1993) Graduate Texts in Mathematics , vol.142
    • Lang, S.1
  • 38
    • 84859638402 scopus 로고    scopus 로고
    • Asset pricing with matrix affine jump diffusions
    • University of Zurich-Swiss Banking Institute (ISB)
    • LEIPPOLD, M. and TROJANI, F. (2008). Asset pricing with matrix affine jump diffusions. Working paper, University of Zurich-Swiss Banking Institute (ISB).
    • (2008) Working paper
    • Leippold, M.1    Trojani, F.2
  • 39
    • 78751578996 scopus 로고    scopus 로고
    • A characterization of the martingale property of exponentially affine processes
    • MAYERHOFER, E., MUHLE-KARBE, J. and SMIRNOV, A. G. (2011). A characterization of the martingale property of exponentially affine processes. Stochastic Process. Appl. 121 568-582.
    • (2011) Stochastic Process. Appl. , vol.121 , pp. 568-582
    • Mayerhofer, E.1    Muhle-Karbe, J.2    Smirnov, A.G.3
  • 40
    • 79953267069 scopus 로고    scopus 로고
    • On strong solutions for positive definite jump-diffusions. VIF Working Paper No. 30
    • MAYERHOFER, E., PFAFFEL, O. and STELZER, R. (2009). On strong solutions for positive definite jump-diffusions. VIF Working Paper No. 30, Vienna Institute of Finance.
    • (2009) Vienna Institute of Finance
    • Mayerhofer, E.1    Pfaffel, O.2    Stelzer, R.3
  • 44
    • 0004267646 scopus 로고    scopus 로고
    • Princeton Univ. Press, Princeton, NJ. MR1451876
    • ROCKAFELLAR, R. T. (1997). Convex Analysis. Princeton Univ. Press, Princeton, NJ. MR1451876
    • (1997) Convex Analysis
    • Rockafellar, R.T.1
  • 46
    • 0004057553 scopus 로고
    • 2nd ed. McGraw-Hill, New York. MR1157815
    • RUDIN, W. (1991). Functional Analysis, 2nd ed. McGraw-Hill, New York. MR1157815
    • (1991) Functional Analysis
    • Rudin, W.1
  • 47
    • 0003232762 scopus 로고    scopus 로고
    • Lévy processes and infinitely divisible distributions
    • Cambridge Univ. Press, Cambridge. MR1739520
    • SATO, K.-I. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge Studies in Advanced Mathematics 68. Cambridge Univ. Press, Cambridge. MR1739520
    • (1999) Cambridge Studies in Advanced Mathematics , vol.68
    • Sato, K.-I.1
  • 49
    • 0004105622 scopus 로고
    • Random processes with independent increments
    • Kluwer Academic, Dordrecht. MR1155400
    • SKOROHOD, A. V. (1991). Random Processes with Independent Increments. Mathematics and Its Applications (Soviet Series) 47. Kluwer Academic, Dordrecht. MR1155400
    • (1991) Mathematics and Its Applications (Soviet Series) , vol.47
    • Skorohod, A.V.1
  • 50
    • 0039435679 scopus 로고
    • A special property of the matrix Riccati equation
    • MR0342748
    • STOKES, A. N. (1974). A special property of the matrix Riccati equation. Bull. Austral. Math. Soc. 10 245-253. MR0342748
    • (1974) Bull. Austral. Math. Soc. , vol.10 , pp. 245-253
    • Stokes, A.N.1
  • 51
    • 0000775921 scopus 로고
    • Diffusion processes associated with lévy generators
    • MR0433614
    • STROOCK, D. W. (1975). Diffusion processes associated with Lévy generators. Z. Wahrsch. Verw. Gebiete 32 209-244. MR0433614
    • (1975) Z. Wahrsch. Verw. Gebiete , vol.32 , pp. 209-244
    • Stroock, D.W.1
  • 52
    • 0013300338 scopus 로고
    • Über die invarianz konvexer mengen und differentialungleichungen in einem normierten raume
    • MR0322305
    • VOLKMANN, P. (1973). Über die Invarianz konvexer Mengen und Differentialungleichungen in einem normierten Raume. Math. Ann. 203 201-210. MR0322305
    • (1973) Math. Ann. , vol.203 , pp. 201-210
    • Volkmann, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.