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Research Papers

G-expected utility maximization with ambiguous equicorrelation

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Pages 403-419 | Received 23 Jun 2019, Accepted 29 May 2020, Published online: 28 Jul 2020

References

  • Bates, D.J. , Hauenstein, J.D. , Sommese, A.J. and Wampler, C.W. , Numerically Solving Polynomial Systems with Bertini, no. 25. In Software, Environments, and Tools, 2013, SIAM.
  • Bernoulli, D. , Exposition of a new theory on the measurement of risk. Econometrica , 1954, 22 , 23. doi: 10.2307/1909829
  • Biagini, S. and Pınar, M.Ç. , The robust Merton problem of an ambiguity averse investor. Math. Financ. Econom. , 2017, 11 , 1–24. doi: 10.1007/s11579-016-0168-6
  • Buchberger, B. , Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. J. Symb. Comput. , 2006, 41 , 475–511. doi: 10.1016/j.jsc.2005.09.007
  • Clements, A. , Scott, A. and Silvennoinen, A. , On the benefits of equicorrelation for portfolio allocation. J. Forecast. , 2015, 34 , 507–522. doi: 10.1002/for.2357
  • Elton, E.J. and Gruber, M.J. , Estimating the dependence structure of share prices–Implications for portfolio selection. J. Finance. , 1973, 28 , 1203–1232.
  • Engle, R. and Kelly, B. , Dynamic equicorrelation. J. Bus. Econ. Stat. , 2012, 30 , 212–228. doi: 10.1080/07350015.2011.652048
  • Epstein, L.G. and Ji, S. , Ambiguous volatility and asset pricing in continuous time. Rev. Financ. Stud. , 2013, 26 , 1740–1786. doi: 10.1093/rfs/hht018
  • Epstein, L.G. and Ji, S. , Ambiguous volatility, possibility and utility in continuous time. J. Math. Econom. , 2014, 50 , 269–282. doi: 10.1016/j.jmateco.2013.09.005
  • Fouque, J.P. , Pun, C.S. and Wong, H.Y. , Portfolio optimization with ambiguous correlation and stochastic volatilities. SIAM J. Control Optim. , 2016, 54 , 2309–2338. doi: 10.1137/15M1032533
  • Fouque, J.P. , Sircar, R. and Zariphopoulou, T. , Portfolio optimization and stochastic volatility asymptotics. Math. Finance , 2017, 27 , 704–745. doi: 10.1111/mafi.12109
  • Gilboa, I. and Schmeidler, D. , Maxmin expected utility with non-unique prior. J. Math. Econom. , 1989, 18 , 141–153. doi: 10.1016/0304-4068(89)90018-9
  • Hansen, L.P. , Sargent, T.J. , Turmuhambetova, G. and Williams, N. , Robust control and model misspecification. J. Econ. Theory. , 2006, 128 , 45–90. doi: 10.1016/j.jet.2004.12.006
  • Hu, M. and Ji, S. , Dynamic programming principle for stochastic recursive optimal control problem driven by a G-Brownian motion.  Their Applications Stoch. Process. Their. Appl. , 2017, 127 , 107–134. doi: 10.1016/j.spa.2016.06.002
  • Hu, M. , Ji, S. and Yang, S. , A stochastic recursive optimal control problem under the G-expectation framework. Appl. Math. Optim. , 2014, 70 , 253–278. doi: 10.1007/s00245-014-9242-8
  • Ismail, A. and Pham, H. , Robust markowitz mean-variance portfolio selection under ambiguous covariance matrix. Math. Finance , 2019, 29 , 174–207. doi: 10.1111/mafi.12169
  • Ledoit, O. and Wolf, M. , Honey, I shrunk the sample covariance matrix. J. Portfolio Manage. , 2004, 30 , 110–119. doi: 10.3905/jpm.2004.110
  • Lei, Q. and Pun, C.S. , An extended McKean–Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix, 2020. Available online at: https://ssrn.com/abstract=3581429 (accessed 16 May 2020).
  • Lin, Q. and Riedel, F. , Optimal consumption and portfolio choice with ambiguity, 2014. Available online at: https://arxiv.org/abs/1401.1639 (accessed 8 January 2014).
  • Mastrolia, T. and Possama, D. , Moral hazard under ambiguity. J. Optim. Theory. Appl. , 2018, 179 , 452–500. doi: 10.1007/s10957-018-1230-8
  • Matoussi, A. , Mezghani, H. and Mnif, M. , Robust utility maximization under convex portfolio constraints. Appl. Math. Optim. , 2014, 71 , 313–351. doi: 10.1007/s00245-014-9259-z
  • Matoussi, A. , Possama, D. and Zhou, C. , Robust utility maximization in nondominated models with 2BSDE: The uncertain volatility model. Math. Finance , 2015, 25 , 258–287. doi: 10.1111/mafi.12031
  • Merton, R.C. , Optimum consumption and portfolio rules in a continuous-time model. J. Econ. Theory. , 1971, 3 , 373–413. doi: 10.1016/0022-0531(71)90038-X
  • Michaud, R.O. , The markowitz optimization enigma: Is ‘optimized’ optimal? Financ. Anal. J. , 1989, 45 , 31–42. doi: 10.2469/faj.v45.n1.31
  • Nutz, M. , Utility maximization under model uncertainty in discrete time. Math. Finance , 2014, 26 , 252–268. doi: 10.1111/mafi.12068
  • Peng, S. , G-Expectation, G-Brownian motion and related stochastic calculus of Itô type. In Stochastic Analysis and Applications, pp. 541–567, 2007 (Springer: Berlin).
  • Peng, S. , Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation. Stoch. Proc. Appl. , 2008, 118 , 2223–2253. doi: 10.1016/j.spa.2007.10.015
  • Peng, S. , Nonlinear Expectations and Stochastic Calculus Under Uncertainty , 95, 2019 (Springer: Berlin).
  • Pham, H. , Wei, X. and Zhou, C. , Portfolio diversification and model uncertainty: A robust dynamic mean-variance approach, 2018. Available online at: https://arxiv.org/abs/1809.01464 (accessed 5 September 2018).
  • Pun, C.S. , Robust time-inconsistent stochastic control problems. Automatica , 2018, 94 , 249–257. doi: 10.1016/j.automatica.2018.04.038
  • Pun, C.S. , Siu, C.C. and Wong, H.Y. , Non-zero-sum reinsurance games subject to ambiguous correlations. Oper. Res. Lett. , 2016, 44 , 578–586. doi: 10.1016/j.orl.2016.06.004
  • Pun, C.S. and Wong, H.Y. , Robust investment–reinsurance optimization with multiscale stochastic volatility. Insur. Math. Econom. , 2015, 62 , 245–256. doi: 10.1016/j.insmatheco.2015.03.030
  • Pun, C.S. and Wong, H.Y. , Robust non-zero-sum stochastic differential reinsurance game. Insur. Math. Econom. , 2016, 68 , 169–177. doi: 10.1016/j.insmatheco.2016.02.007
  • von Neumann, J. and Morgenstern, O. , Theory of Games and Economic Behavior , 1944 (Princeton University Press: Princeton, NJ).
  • Wald, A. , Statistical decision functions which minimize the maximum risk. Ann. Math. , 1945, 46 , 265. doi: 10.2307/1969022
  • Yong, J. and Zhou, X.Y. , Stochastic Controls: Hamiltonian Systems and HJB Equations , 1999 (Springer: New York).
  • Zhou, X.Y. and Li, D. , Continuous-Time mean-variance portfolio selection: A stochastic LQ framework. Appl. Math. Optim. , 2000, 42 , 19–33. doi: 10.1007/s002450010003

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