Risk-Sensitive Asset Management under a Wishart Autoregressive Factor Model

DOI: 10.4236/jmf.2013.31A021   PDF   HTML     4,254 Downloads   7,171 Views   Citations


The risk-sensitive asset management problem with a finite horizon is studied under a financial market model having a Wishart autoregressive stochastic factor, which is positive-definite symmetric matrix-valued. This financial market model has the following interesting features: 1) it describes the stochasticity of the market covariance structure, interest rates, and the risk premium of the risky assets; and 2) it admits the explicit representations of the solution to the risk-sensitive asset management problem.

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H. Hata and J. Sekine, "Risk-Sensitive Asset Management under a Wishart Autoregressive Factor Model," Journal of Mathematical Finance, Vol. 3 No. 1A, 2013, pp. 222-229. doi: 10.4236/jmf.2013.31A021.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] T. R. Bielecki and S. R. Pliska, “Risk Sensitive Dynamic Asset Management,” Applied Mathematics and Optimization, Vol. 39, No. 3, 1999, pp. 337-360. doi:10.1007/s002459900110
[2] T. R. Bielecki and S. R. Pliska, “Risk Sensitive Intertemporal CAPM, with Application to Fixed-Income Management,” IEEE Transactions on Automat. Control, Vol. 49, No. 3, 2004, pp. 420-432. doi:10.1109/TAC.2004.824470
[3] M. H. A. Davis and S. Lleo, “Risk-Sensitive Benchmarked Asset Management,” Quantitative Finance, Vol. 8, No. 4, 2008, pp. 415-426.
[4] W. H. Fleming and S. J. Sheu, “Risk-Sensitive Control and an Optimal Investment Model,” Mathematical Finance, Vol. 10, No. 2, 2000, pp. 197-213. doi:10.1111/1467-9965.00089
[5] W. H. Fleming and S. J. Sheu, “Risk-Sensitive Control and an Optimal Investment Model. II,” Annals of Applied Probability, Vol. 12, No. 2, 2002, pp. 730-767. doi:10.1214/aoap/1026915623
[6] H. Hata, H. Nagai and S. J. Sheu, “Asymptotics of the Probability Minimizing a ‘Down-Side’ Risk,” Annals of Applied Probability., Vol. 20, No. 1, 2010, pp. 52-89. doi:10.1214/09-AAP618
[7] K. Kuroda and H. Nagai, “Risk Sensitive Portfolio Optimization on Infinite Time Horizon,” Stochastics and Stochastics Reports, Vol. 73, No. 3-4, 2002, pp. 309-331.
[8] M. F. Bru, “Wishart Processes,” Journal of Theoretical Probability, Vol. 4, No. 4, 1991, pp. 725-751. doi:10.1007/BF01259552
[9] C. Cuchiero, D. Filipovic, E. Mayerhofer and J. Teichmann, “Affine Processes on Positive Semidefinite Matrices,” Annals of Applied Probability, Vol. 21, No. 2, 2011, pp. 397-463. doi:10.1214/10-AAP710
[10] E. Mayerhofer, O. Pfaffel and R. Stelzer, “On Strong Solutions for Positive Definite Jump Diffusions,” Stochastic Processes and Their Applications, Vol. 121, No. 9, 2011, pp. 2072-2086. doi:10.1016/j.spa.2011.05.006
[11] A. Benabid, H. Bensusan and N. El Karoui, “Wishart Stochastic Volatility: Asymptotic Smile and Numerical Framework,” Preprint, 2010.
[12] J. Da Fonseca, M. Grasselli and C. Tebaldi, “Option Pricing When Correlations Are Stochastic: An Analytical Framework,” Review of Derivatives Research, Vol. 10, No. 2, 2007, pp. 151-180. doi:10.1016/j.spa.2011.05.006
[13] J. Da Fonseca, M. Grasselli, and C. Tebaldi, “A Multifactor Volatility Heston Model,” Quantitative Finance, Vol. 8, No. 6, 2008, pp. 591-604. doi:10.1080/14697680701668418
[14] C. Gouriéroux, “Continuous Time Wishart Process for Stochastic Risk,” Econometric Reviews, Vol. 25, No. 2, 2006, pp. 177-217.
[15] C. Gouriéroux, J. Jasiak and R. Sufana, “The Wishart Autoregressive Process of Multivariate Stochastic Volatility,” Journal of Econometrics, Vol. 150, No. 2, 2009, pp. 167-181. doi:10.1016/j.jeconom.2008.12.016
[16] M. Grasselli and C. Tebaldi, “Solvable Affine Term Structure Models,” Mathematical Finance, Vol. 18, No. 1, 2008, pp. 135-153. doi:10.1111/j.1467-9965.2007.00325.x
[17] A. Buraschi, A. Cieslak and F. Trojani, “Correlation Risk and the Term Structure of Interest Rates,” Working Paper, University of St. Gallen, 2008.
[18] A. Buraschi, P. Porchia and F. Trojani, “Correlation Risk and Optimal Portfolio Choice,” Journal of Finance, Vol. 65, No. 1, 2010, pp. 393-420. doi:10.1111/j.1540-6261.2009.01533.x
[19] C. Chiarella, C-Y. Hsiao and T-D. To, “Risk Premia and Wishart Term Structure Models,” Preprint, 2010.
[20] C. Gouriéroux and R. Sufana, “Wishart Quadratic Term Structure Models,” Working Paper, CREF, 03-10, HEC, Montreal, 2003.
[21] D. Duffie, D. Filipovic and W. Schachermayer, “Affine Processes and Applications in Finance,” Annals of Applied Probability, Vol. 13, No. 3, 2003, pp. 984-1053. doi:10.1214/aoap/1060202833
[22] D. Filipovic and E. Mayerhofer, “Affine Diffusion Processes: Theory and Applications,” Radon Series on Computational and Applied Mathematics, Vol. 8, 2009, pp. 125-164. doi:10.1515/9783110213140.125
[23] H. Hata, “Down-Side Risk Probability Minimization Problem with Cox-Ingersoll-Ross’s Interest Rates,” AsiaPacific Financial Markets, Vol. 18, No. 1, 2011, pp. 69-87. doi:10.1007/s10690-010-9121-5
[24] Y. Watanabe, “Asymptotic Analyses for Certain Stochastic Control Problems under Partial Information and the Related Filtering Equation,” Thesis, Graduate School of Engineering Science, Osaka University, 2011.
[25] A. Bensoussan, “Stochastic Control of Partially Observable Systems,” Cambridge University Press, Cambridge, 1992. doi:10.1017/CBO9780511526503

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