A stochastic portfolio optimization model with complete memory

References

• Bielecki, T. R., and Pliska, S. R. 1999. Risk sensitive dynamic asset management. Applied Mathematics and Optimization 37:337–360.
   Web of Science ®Google Scholar
• Bauer, H., and Rieder, U. 2005. Stochastic control problems with delay. Mathematical Methods of Operations Research 62(3):411–427.
   Web of Science ®Google Scholar
• Chang, M. H., Pang, T., and Pemy, M. 2008. Finite difference approximations for stochastic control systems with delay. Stochastic Analysis and Applications 26:451–470.
   Web of Science ®Google Scholar
• Chang, M. H., Pang, T., and Pemy, M. 2008. Optimal control of stochastic functional differential equations with a bounded memory. Stochastics 80:69–96.
   Google Scholar
• Chang, M. H., Pang, T., and Yang, Y. 2011. A stochastic portfolio optimization model with bounded memory. Mathematics of Operations Research 36:604–619.
   Web of Science ®Google Scholar
• Cont, R., and Fournié, D. A. 2013. Functional Ito calculus and stochastic integral representation of martingales. Annuals of Probability 41(1):109–133.
   Web of Science ®Google Scholar
• Chen, L., and Wu, Z. 2010. Maximum principle for the stochastic optimal control problem with delay and application. Automatica 46(6):1074–1080.
   Web of Science ®Google Scholar
• Dupire, B. 2009. Functional Itô’s calculus. Bloomberg Portfolio Research Paper No.2009-04-FRONTIERS. http://ssrn.com/abstract=1435551; http://dx.doi.org/10.2139/ssrn.1435551
   Google Scholar
• Elsanousi, I., and Larssen, B. 2001. Optimal consumption under partial observations for a stochastic system with delay. University of Oslo. http://urn.nb.no/URN:NBN:no-24279 [Preprint]
   Google Scholar
• Elsanousi, I., Øksendal, B., and Sulem, A. 2000. Some solvable stochastic control problems with delay. Stochastics and Stochastics Reports 71:69–89.
   Google Scholar
• Federico, S. 2011. A stochastic control problem with delay arising in a pension fund model. Finance and Stochastics 15(3):421–459.
   Web of Science ®Google Scholar
• Fleming, W. H., and Sheu, S. J. 2000. Risk-sensitive control and optimal investment model. Mathematical Finance 10:197–213.
   Web of Science ®Google Scholar
• Fleming, W. H., and Hernandez-Hernandez, D. 2003. An optimal consumption model with stochastic volatility. Finance and Stochastics 7:245–262.
   Web of Science ®Google Scholar
• Fleming, W. H., and Pang, T. 2004. An application of stochastic control theory to financial economics. SIAM Journal on Control and Optimization 43:502–531.
   Web of Science ®Google Scholar
• Fleming, W. H., and Pang, T. 2005. A stochastic control model of investment, production and consumption. Quarterly of Applied Mathematics 63:71–87.
   Web of Science ®Google Scholar
• Fleming, W. H., and Soner, H. M. 2006. Controlled Markov Processes and Viscosity Solutions. New York: Springer.
   Google Scholar
• Fouque, J. P., Papanicolaou, G., and Sircar, R. 2000. Derivatives in Financial Market with Stochastic Volatility. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Gozzi, F., Marinelli, C., and Savin, S. 2009. On controlled linear diffusions with delay in a model of optimal advertising under uncertainty with memory effects. Journal of Optimization Theory and Applications 142(2):291–321.
   Web of Science ®Google Scholar
• Hata, H., and Sheu, S.-J. 2012. On the Hamilton-Jacobi-Bellman equation for an optimal consumption problem: I. Existence of solution. Journal on Control and Optimization 50:2373–2400.
   Web of Science ®Google Scholar
• Hata, H., and Sheu, S.-J. 2012. On the Hamilton-Jacobi-Bellman equation for an optimal consumption problem: II. Verification theorem. Journal on Control and Optimization 50:2401–2430.
   Web of Science ®Google Scholar
• Karatzas, I., and Shreve, E. S. 1991. Brownian Motion and Stochastic Calculus. New York: Springer.
   Google Scholar
• Koivo, A. J. 1973. Optimal control of linear stochastic systems described by functional differential equations. Journal of Optimization Theory and Applications 9:161–175.
   Google Scholar
• Kolmanovskii, V. B., and Maizenberg, T. L. 1973. Optimal control of stochastic systems with aftereffect. Avtomat. i Telemeh 1:47–61.
   Google Scholar
• Kolmanovskii, V. B., and Shaikhet, L. E. 1996. Control of Systems with Aftereffect. Providence, RI: American Mathematical Society.
   Google Scholar
• Larssen, B. 2002. Dynamic programming in stochastic control of systems with delay. Stochastics 74:651–673.
   Google Scholar
• Larssen, B., and Risebro, N. H. 2003. When are HJB-equations in stochastic control of delay systems finite dimensional. Stochastic Analysis and Applications 2:643–671.
   Web of Science ®Google Scholar
• Lindquist, A. 1973. On feedback control of linear stochastic systems. SIAM Journal on Control 11:323–343.
   Web of Science ®Google Scholar
• Lindquist, A. 1973. Optimal control of linear stochastic systems with applications to time lag systems. Information Sciences 5:81–124.
   Web of Science ®Google Scholar
• Mohammed S.-E. A.1984. Stochastic Functional Differential Equations. Boston: Pitman.
   Google Scholar
• Mohammed S.-E. A.1998. Stochastic differential equations with memory-theory, examples and applications. Stochastics Analysis and Related Topics 6:1–77.
   Google Scholar
• Øksendal, B., and Sulem, A. 2001. A maximum principle for optimal control of stochastic systems with delay with applications to finance. Optimal Control and Partial Differential Equations, Eds. J. L. Menaldi, E. Rofman and A. Sulem, Amsterdam: IOS Press, 64–79.
   Google Scholar
• Øksendal, B., Sulem, A., and Zhang, T. 2011. Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations. Advances in Applied Probability 43:572–596.
   Web of Science ®Google Scholar
• Pang, T. 2004. Portfolio optimization models on infinite-time horizon. Journal of Optimization Theory and Applications 122:573–597.
   Web of Science ®Google Scholar
• Pang, T. 2006. Stochastic portfolio optimization with log utility. International Journal Theory and Applied Finance 9:869–887.
   Google Scholar
• Pang, T., and Hussain, A. 2015. An application of functional Ito’s formula to stochastic portfolio optimization with bounded memory. Proceedings of 2015 SIAM Conference on Control and Its Applications (CT15), July 8–10, Paris, France, 159–166.
   Google Scholar
• Pang, T., and Hussain, A. 2016. An infinite time horizon portfolio optimization model with delays. Mathematical Control and Related Fields 6:629–651.
   Web of Science ®Google Scholar