Stochastic-fractional optimal control problems and application in portfolio management

[1] M. Sanei, S. Banihashemiyz, M. Kaveh, Estimation of portfolio effcient frontier by different
measures of risk via DEA, Int.J.Industrial Mathematics, Vol. 8,(2016), pp.10.
[2] F. Kircher, D. Rosch, A shrinkage approach for Sharpe ratio optimal portfolios with estimation risks, Journal of Banking Finance, Vol.133, (2021), pp.
[3] F.Oreste, Quantum trading, John Wiley Sons, Inc., Hoboken, New Jersey (2011), pp.29-33.
[4] D. S. Ehrman, The handbook of pairs trading, John Wiley Sons, Inc., Hoboken, New Jersey
(2006), pp.1-272.
[5] S. Mudchanatongsuk, J. A. Primbs, W. Wong, Optimal pairs trading: A stochastic control
approach, IEEE, Conference Location: Seattle, WA, USA, , (2008), pp.1035–1039.
[6] S.Chen, J.Yong, Stochastic linear quadratic optimal control problems, Appl Math Optim,
Vol.43(1), (2001), pp.21-45.
[7] E.Rouy, A.Tourin, A viscosity solutions approach to shape-from-shading, SIAM J. Numer.
Anal, Vol.29(3), pp.1-19, (2004).
[8] H.Kappen, path integrals symetry breaking for optimal control theory, Journal of Statistical mechanics: theory and experience, (1992), pp.11011.
[9] B.Balaji, Continuous-discrete path integral filtering, enteropy, Vol.11, (2013), pp.402-
430.
[10] E.J. Elton, Martin J. Gruber, Modern Portfolio Theory and Investment Analysis, 361,
John Wiley Sons,(1995).
[11] H.Geering, F. Herzog, G. Dondi, Stochastic Optimal Control with Applications in Financial Engineering, Springer optimization and its applications, Vol.39, (2010), pp.375 -
408.
[12] J.Pholipper, Risk2: Measuring the Riak in Value at Risk, Financial Analysts Journal,(1996), pp.47-56.
[13] W. F. Sharpe, Mutual Fund Performance, Journal of Business, Vol.39, (1966), pp.119-
138.
[14] L.Kopman, S. Liu, Maximizing the Sharpe Ratio and Information Ratio in the Barra Optimizer, Journal of Business, pp.14, (2009).
[15] A.Al-Aradi, S. Jaimungal, Outperformance and Tracking: Dynamic Asset Allocation for
Active and Passive Portfolio Management, Applied Mathematical Finance, , (2018),
pp.33.
[16] O.P.Agrawal, A general formulation and solution scheme for fractional optimal control
problems, Nonlinear Dyn. Vol.38(1), (2004), pp.323337.
[17] An Li, E. Feng, X. Sun, Stochastic optimal control and algorithm of the trajectory of horizontal wells, Journal of Computational and Applied Mathematics , Vol.212 ,(2008),
pp. 419 430.
[18] F. Pourofoghi, D. Darvishi Salokolaei, Solving linear fractional programming problems
in uncertain environments: A novel approach with grey parameters, Control and Optimization in Applied Mathematics, Vol.9(1), (2024), pp.169-183.