McKean-Vlasov limit in portfolio optimization

Stochastic Analysis and Applications

Volumn 28, Issue 5, 2010, Pages 884-906

  Borkar, V S ^a   Kumar, K Suresh ^b  

^a TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

^b INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

Author keywords

Mckean vlasov equation; Nonlinear parabolic equation; Portfolio optimization

Indexed keywords

EID: 77955647213     PISSN: 07362994     EISSN: 15329356     Source Type: Journal    
DOI: 10.1080/07362994.2010.482836     Document Type: Article

References (15)

1. Bensoussan, A. 1982. Stochastic Control by Functional Analysis Methods, Studies in Mathematics and Its Applications, North-Holland, New York.
2. Bielecki, T.R., and Pliska, S.R. 1999. Risk-sensitive dynamic asset management, Applied Mathematics and Optimization 39:337-360.
3. Fabes, E., and Kenig C. 1981. Examples of singular probability measures and singular transition probability densities. Duke Mathematics Journal 48:845-856.
4. Horst, U. 2002. Asymptotics of locally interacting Markov chains with global signals. Advances in Applied Probability 34:1-25.
5. Ikeda, N., and Watanabe, S. 1989. Stochastic Differential Equations and Diffusion Processes, 2nd Edition, North Holland, Amsterdam.
6. Kac, M. 1956. Foundations of kinetic theory. In Proceedings of the 3rd Berkeley Symposium on Mathematics Statistics and Probability. Neyman, J. (ed.), University of California Press, Berkeley, CA, pp. 171-197.
7. Kac, M. 1959. Probability and Related Topics in Physical Sciences, Interscience Publishers, London.
8. Lasry, J.-M., and Lions, P.-L. 2007. Mean field games, Japanese Journal of Mathematics 2:229-260.
9. Leonard, C. 1986. Une loi des grands nombres pour des systèmes de diffusions avec interaction et à coefficients non bornés, Ann. Inst. Henri. Poincaré: Probabilités et Statistiques 22:237-262.
10. McKean, H.P. 1969. Propagation of chaos for a class of nonlinear parabolic equations. In Lecture Series in Differential Equations 2. Aziz, A.K. (ed.), Van Nostrand Rheinhold, New York.
11. McKean, H.P. 1966. A class of Markov processes associated with nonlinear parabolic equations. Proc. Nat. Acad. Sci. 56:1907-1911.
12. Merton, R.C. 1971. Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3:373-413.
13. Rogers, L.C.G., and Williams, D. 2000. Diffusions, Markov Processes and Martingales, Vol. 2, Cambridge University Press, UK.
14. Stroock, D.W., and Varadhan, S.R.S. 1979. Multidimensional Diffusion Processes, Springer Verlag, New York.
15. Sznitman, A.S. 1991. Topics in propogation of chaos, in 'Ecole dété de Probabilités de Saint Flour (1989)', Springer Lecture Notes in Mathematics No. 1464, pp. 166-251.