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On the multi-dimensional portfolio optimization with stochastic volatility

Pages 27-40 | Received 17 Oct 2014, Published online: 15 Sep 2017

References

  • Y. Aktar and E. Taflin, A remark on smooth solutions to a stochastic control problem with a power terminal cost function and stochastic volatilities, Math. Finan. Econ. >8 (2014), 489–509. doi: 10.1007/s11579-014-0128-y
  • F.E. Benth and K. Karlsen, A PDE representation of the density of the minimum entropy martingale measure in stochastic volatility markets, Stochastics: An International Journal of probability and Stochastic Processes >77(2) (2005), 109–137.
  • J. Fan, J. Jiang, C Zhang and Z. Zhou, Time-dependent diffusion models for term structure dynamics, Statistica Sinica >13 (2003), 965–992.
  • D. Filipović, Time-inhomogeneous affine processes, Stochastic Processes and their Applications >115(4) (2005), 639–659. doi: 10.1016/j.spa.2004.11.006
  • D. Filipović and J. Teichmann, On the geometry of the term structure of interest rates, Proceedings: Mathematical, Physical and Engineering Sciences >460(2041) (2004), 129–167.
  • W.H. Fleming, Exit probabilities and optimal stochastic control, Appl. Math. Optim. >4 (1978), 329–346. doi: 10.1007/BF01442148
  • W.H. Fleming and R. Rishel, Deterministic and stochastic optimal control, Springer-Verlag, New York, 1975.
  • W.H. Fleming and H.M. Soner, Controlled Markov processes and viscosity solutions, Springer-Verlag, New York, 1993.
  • S.L. Heston, A closed form solution for options with stochastic volatility with applications to bond and currency options, The Review of Financial Studies >6 (1993), 327–343. doi: 10.1093/rfs/6.2.327
  • D. Hobson, Stochastic volatility models, correlation, and the q-optimal measure, Mathematical Finance >14(4) (2004), 537–556. doi: 10.1111/j.0960-1627.2004.00204.x
  • J. Hull and A. White, The pricing of options on assets with stochastic volatilities, Journal of Finance >42 (1987), 281–300. doi: 10.1111/j.1540-6261.1987.tb02568.x
  • I. Karatzas, Lectures on the Mathematics of Finance, CRM Monograph Series, Vol. 8, American Mathematical Society, Providence, RI, 1997.
  • R. Kufakunesu, The density process of the minimal entropy martingale measure in a stochastic volatility market: A PDE approach, Quaestiones Mathematicae >34(4) (2011), 147–174. doi: 10.2989/16073606.2011.594229
  • R. Kufakunesu, Optimal investment models with stochastic volatility and portfolio constraints: the time inhomogeneous case, Quaestiones Mathematicae >38(2) (2015), 237–255. doi: 10.2989/16073606.2014.981701
  • R. Liptser and A. Shiryaev, Statistics of random processes, Vol. >1, Springer-Verlag, New York, 1977.
  • Y. Maghosoodi, Solution of the extended CIR term structure and bond valuation, Mathematical Finance >6(1) (1996), 89–109. doi: 10.1111/j.1467-9965.1996.tb00113.x
  • R. Merton, Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory >3 (1971), 373–413. doi: 10.1016/0022-0531(71)90038-X
  • M. Mnif, Portfolio optimization with stochastic volatilities and constraints: An application in high dimension, Appl. Math. Optim. >56 (2007), 243–264. doi: 10.1007/s00245-007-0896-3
  • H. Pham, Smooth solutions to optimal investment models with stochastic volatilities and portfolio constraints, Appl. Math. Optim. >45 (2002), 55–78. doi: 10.1007/s00245-002-0735-5
  • F. Protter, Stochastic integration and differential equations: Version 2.1, A new approach, Springer-Verlag, New York, 2000.
  • L.O. Scott, Option pricing when the variance changes randomly: theory, estimation, and an application, Journal of Financial and Quantitative Analysis >22 (1987), 419–438. doi: 10.2307/2330793
  • E. Stein and J. Stein, Stock price distributions with stochastic volatility, The Review of Financial Studies >4 (1991), 727–752. doi: 10.1093/rfs/4.4.727
  • T. Zariphopoulou, Consumption investment models with constraints, SIAM J. Control and Optimization >32(1) (1994), 59–85. doi: 10.1137/S0363012991218827
  • T. Zariphopoulou, A solution approach to valuation with unhedgeable risks, Finance and Stochast. >5 (2001), 61–82. doi: 10.1007/PL00000040

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