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Research Papers

HARA utility maximization in a Markov-switching bond–stock market

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Pages 1715-1733 | Received 05 Jun 2016, Accepted 24 Feb 2017, Published online: 18 Jul 2017

References

  • Aït-Sahalia, Y. and Kimmel, R., Maximum likelihood estimation of stochastic volatility models. J. Financ. Econ., 2007, 83, 413–452.
  • Andersson, M., Krylova, E. and Vähämaa, S., Why does the correlation between stock and bond returns vary over time? Appl. Financ. Econ., 2008, 18, 139–151.
  • Ang, A. and Bekaert, G., Stock return predictability: Is it there? Rev. Financ. Stud., 2007, 20, 651–707.
  • Babbs, S.H. and Nowman, K.B., Kalman filtering of generalized Vasicek term structure models. J. Financ. Quant. Anal., 1999, 34, 115–130.
  • Baele, L., Bekaert, G. and Inghelbrecht, K., The determinants of stock and bond return comovements. Rev. Financ. Stud., 2010, 23, 2374–2428.
  • Bäuerle, N. and Li, Z., Optimal portfolios for financial markets with Wishart volatility. J. Appl. Probab., 2013, 50, 1025–1043.
  • Bäuerle, N. and Rieder, U., Portfolio optimization with Markov-modulated stock prices and interest rates. Autom. Control, 2004, 49, 442–447.
  • Baum, L.E., Petrie, T., Soules, G. and Weiss, N., A maximization technique occuring in the statistical analysis of probabilistic functions of Markov chains. Ann. Math. Stat., 1970, 41, 164–171.
  • Bernhart, G., Höcht, S., Neugebauer, M., Neumann, M. and Zagst, R., Asset correlations in turbulent markets and the impact of different regimes on asset management. Asia-Pac. J. Oper. Res., 2011, 28, 1–23.
  • Black, F. and Jones, R., Simplifying portfolio insurance. J. Portfolio Manage., 1987, 14, 48–51.
  • Black, F. and Perold, A., Theory of constant proportion portfolio insurance. J. Econ. Dyn. Control, 1992, 16, 403–426.
  • Bollerslev, T., Engle, R.F. and Wooldridge, J.M., A capital asset pricing model with time-varying covariances. J. Polit. Econ., 1988, 96, 116–131.
  • Brennan, M.J. and Xia, Y., Stochastic interest rates and the bond-stock mix. Eur. Finance Rev., 2000, 4, 197–210.
  • Çanakoğlu, E. and Özekici, S., Portfolio selection in stochastic markets with HARA utility functions. Eur. J. Oper. Res., 2010, 201, 520–536.
  • Çanakoğlu, E. and Özekici, S., HARA frontiers of optimal portfolios in stochastic markets. Eur. J. Oper. Res., 2012, 221, 129–137.
  • Chen, R. and Scott, L., Multi-factor Cox--Ingersoll--Ross models of the term structure: Estimates and tests from a Kalman Filter model. J. Real Estate Financ, 2003, 27, 143–172.
  • Chen, S., Predicting the bear stock market: Macroeconomic variables as leading indicators. J. Bank. Financ, 2009, 33, 211–223.
  • Choi, S., Regime-switching univariate diffusion models of the short-term interest rate. Stud. Nonlinear Dyn. Econ., 2009, 13, 1–41.
  • Choi, S. and Yuan, D., Continuous time stochastic volatility models with regime shifts. Working Paper, 2013.
  • Cont, R. and da Fonseca, J., Dynamics of implied volatility surfaces. Quant. Finance, 2002, 2, 45–60.
  • Durham, G. and Park, Y., Beyond stochastic volatility and jumps in returns and volatility. J. Bus. Econ. Stat., 2013, 31, 107–121.
  • Elliott, R.J., Aggoun, L. and Moore, J., Hidden Markov Models, 1st ed.., 1995 (Springer Verlag: New York).
  • Elliott, R.J. and Nishide, K., Pricing of discount bonds with a Markov switching regime. Ann. Financ, 2014, 10, 509–522.
  • Elliott, R.J. and Siu, T.K., Robust optimal portfolio choice under a Markovian regime switching model. Methodol. Comput. Appl. Probab., 2009, 11, 145–157.
  • Elliott, R.J. and Siu, T.K., On risk minimizing portfolios under a Markovian regime-switching Black--Scholes economy. Ann. Oper. Res., 2010, 176, 271–291.
  • Elliott, R.J. and Siu, T.K., A stochastic differential game for optimal investment of an insurer with regime switching. Quant. Finance, 2011, 11, 365–380.
  • Elliott, R.J., Siu, T.K. and Chan, L., Pricing volatility swaps under Heston’s stochastic volatility model with regime switching. Appl. Math. Financ, 2007, 14, 41–62.
  • Engle, R., What good is a volatility model? Quant. Finance, 2001, 1, 237–245.
  • Erlwein, C. and Mamon, R., An online estimation scheme for a Hull--White model with HMM-driven parameters. Stat. Method Appl., 2009, 18, 87–107.
  • Escobar, M., Götz, B., Neykova, D. and Zagst, R., Stochastic correlation and volatility mean-reversion -- empirical motivation and derivatives pricing via perturbation theory. Appl. Math. Financ, 2014, 21, 555–594.
  • Escobar, M., Neykova, D. and Zagst, R., Portfolio optimization in affine models with Markov switching. Int. J. Theor. Appl. Financ, 2015, 18, 1–44.
  • Fouque, J.P., Papanicolaou, G. and Sircar, K.R., Mean-reverting stochastic volatility. Int. J. Theor. Appl. Financ, 2000, 3, 101–142.
  • Frauendorfer, K., Jacoby, U. and Schwendener, A., Regime switching based portfolio selection for pension funds. J. Bank. Financ, 2007, 31, 2265–2280.
  • Grzelak, L.A. and Oosterlee, C.W., On the Heston model with stochastic interest rates. SIAM J. Financ. Math., 2011, 2, 255–286.
  • Harvey, A., Forecasting, Structural Time Series Models and the Kalman Filter, 1st ed., 1989 (Cambridge University Press: Cambridge).
  • Hata, H. and Sekine, J., Risk-sensitive ssset management under a Wishart autoregressive factor model. J. Math. Financ, 2013, 3, 222–229.
  • Hauptmann, J., Hoppenkamps, A., Min, A., Ramsauer, F. and Zagst, R., Forecasting market turbulence using regime-switching models. Financ. Mark. Portf. Manage., 2014, 28, 139–164.
  • Heston, S., A closed-form solution for options with stochastic volatility with applications to bond and currency options. J. Financ, 1993, 42, 327–343.
  • Höcht, S., Wolf, K.H.N. and Zagst, R., Optimal portfolio allocation with Asian Hedge Funds and Asian REITs. Int. J. Serv. Sci., 2008, 1, 36–68.
  • Jacod, J. and Shiryaev, A., Limit Theorems for Stochastic Processes, 2nd ed., 2003 (Springer Verlag: Heidelberg).
  • Johnson, N., Naik, V., Page, S., Pedersen, N. and Sapra, S. The stock-bond correlation. Working Paper, Pimco Quantitative Research, 2013.
  • Kallsen, J. and Muhle-Karbe, J., Exponentially affine martingales, affine measure changes and exponential moments of affine processes. Stoch. Processes Appl., 2010a, 120, 163–181.
  • Kallsen, J. and Muhle-Karbe, J., Utility maximization in affine stochastic volatility models. Int. J. Theor. Appl. Financ, 2010b, 13, 459–477.
  • Kalman, R.E., New approach to linear filtering and prediction problems. J. Basic Eng.-T ASME 1960, 82, 35–45.
  • Kalman, R.E. and Buchy, R.S., New results in linear filtering and prediction theory. J. Basic Eng.-T ASME, 1961, 83, 95–107.
  • Korn, R., Optimal portfolios with a positive lower bound on final wealth. Quant. Finance, 2005, 5, 315–321.
  • Korn, R. and Kraft, H., A stochastic control approach to portfolio problems with stochastic interest rates. SIAM J. Control Optim., 2001, 40, 1250–1269.
  • Kraft, H., Optimal portfolios and Heston’s stochastic volatility model. Quant. Finance, 2005, 5, 303–313.
  • Kraft, H. and Steffensen, M., A dynamic programming approach to constrained portfolios. Eur. J. Oper. Res., 2013, 229, 453–461.
  • Liu, J., Portfolio selection in stochastic environments. Rev. Financ. Stud., 2007, 20, 1–39.
  • Maheu, J.M. and McCurdy, T.H., Identifying bull and bear markets in stock returns. J. Bus. Econ. Stat., 2000, 18, 100–112.
  • Merton, R.C., Optimum consumption and portfolio rules in a continuous time model. J. Econ. Theory, 1971, 3, 373–413.
  • Mitra, S., Regime switching stochastic volatility option pricing. J. Financ. Markets Deriv., 2010, 1, 213–242.
  • Neykova, D., Escobar, M. and Zagst, R., Optimal investment in multidimensional Markov-modulated affine models. Ann. Financ, 2015, 11, 503–530.
  • Papanicolaou, A. and Sircar, R., A regime-switching Heston model for VIX and S &P 500 implied volatilities. Quant. Finance, 2013, 19, 1–7.
  • Perold, A.F., Constant proportion portfolio insurance. Harvard Business School, August 1986.
  • Perold, A.F. and Sharpe, W.F., Dynamic strategies for asset allocation. Financ. Anal. J., 1988, 44, 16–27.
  • Pham, H., Continuous-time Stochastic Control and Optimization with Financial Applications, 1st ed., 2009 (Springer-Verlag: Berlin Heidelberg).
  • Recchioni, M.C. and Sun, Y., An explicitly solvable Heston model with stochastic interest rate. Eur. J. Oper. Res., 2016, 249, 359–377.
  • Rubinstein, M., Nonparametric tests of alternative option pricing models using all reported trades and quotes on the 30 most active CBOE option classes from August 23, 1976 through August 31, 1978. J. Financ, 1985, 40, 455–480.
  • Sangvinatsos, A. and Wachter, J.A., Does the failure of the expectations hypothesis matter for long-term investors? J. Financ, 2005, 60, 179–230.
  • Santos, T. and Veronesi, P., Labor income and predictable stock returns. Rev. Financ. Stud., 2006, 19, 1–44.
  • Schönbucher, P.J., Credit Derivatives Pricing Models, 1st ed., 2003 (John Wiley & Sons Ltd: Chichester).
  • Sotomayor, L.R. and Cadenillas, A., Explicit solutions of consumption-investment problems in financial markets with regime switching. Math. Finance, 2009, 19, 251–279.
  • Teplá, L., Optimal investment with minimum performance constraints. J. Econ. Dyn. Control, 2001, 25, 1629–1645.
  • Vasicek, O., An equilibrium characterization of the term structure. J. Financ. Econ., 1977, 5, 177–188.
  • Wu, J.L. and Chen, S.L., Mean reversion of interest rates in the eurocurrency market. Oxford Bull. Econ. Stat., 2001, 63, 459–473.
  • Zagst, R. and Kraus, J., Stochastic dominance of portfolio insurance strategies. Ann. Oper. Res., 2011, 185, 75–103.
  • Zhou, N. and Mamon, R., An accessible implementation of interest rate models with Markov-switching. Expert. Syst. Appl., 2012, 39, 4679–4689.
  • Zucchini, W. and MacDonald, I.L., Hidden Markov Models for Time Series: An Introduction Using R, 1st ed., 2009 (Chapman and Hall/CRC Press: Boka Raton, FL).

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