Instantaneous Mean-Variance Hedging and Sharpe Ratio Pricing in a Regime-Switching Financial Model

References

• Barles, G.; Buckdahn, R.; Pardoux, E. Backward stochastic differential equations and integral-partial differential equations. Stochastic and Stochastic Reports 1997, 60, 57–83.
   Google Scholar
• Bayraktar, E.; Young, V. Pricing options in incomplete equity markets via the instantaneous Sharpe ratio. Ann. Finance 2008, 4, 399–429.
   Google Scholar
• Bayraktar, E.; Milevsky, M.; Promislow, S.; Young, V. Valuation of mortality risk via the instantaneous Sharpe ratio: applications to life annuities. J. Econ. Dynamic Control 2009, 33, 676–691.
   Web of Science ®Google Scholar
• Becherer, D. Bounded solutions to BSDE’s with jumps for utility optimization and indifference hedging. Ann. Appl. Probab. 2006, 16, 2027–2054.
   Web of Science ®Google Scholar
• Becherer, D. From bounds on optimal growth towards a theory of good-deal hedging. In Advanced Financial Modelling; Albecher, H.; Runggaldier, W.; Schachermayer, W., Eds.; Walter de Gruyter: Berlin, 2009; 27–52.
   Google Scholar
• Björk, T.; Slinko, I. Towards a general theory of good deal bounds. Rev. Finance 2006, 10, 221–260.
   Google Scholar
• Bouchard, B.; Elie, R. Discrete time approximation of decoupled forward backward SDE with jumps. Stoch. Proc. Appl. 2008, 118, 53–75.
   Web of Science ®Google Scholar
• Cochrane, J.; Saá-Requejo, J. Beyond arbitrage: good-deal asset price bounds in incomplete markets. J. Polit. Econ. 2008, 1008, 79–119.
   Google Scholar
• Crépey, S. About the pricing equation in finance. In Paris-Princeton Lectures in Mathematical Finance 2010; Carmona, R.A.; Çinlar, E.; Ekeland, I.; Jouini, E.; Scheinkman, J.A.; Touzi, N., Eds.; Springer Verlag: Berlin, 2011; 63–203.
   Google Scholar
• Crépey, S. Financial Modeling: A Backward Stochastic Differential Equations Perspective; Springer Verlag: Berlin, 2013.
   Google Scholar
• Delong, Ł. No-good-deal, local mean-variance and ambiguity risk pricing and hedging for an insurance payment process. ASTIN Bull. 2011, 42, 203–232.
   Web of Science ®Google Scholar
• Delong, Ł. Backward Stochastic Differential Equations with Jumps and their Actuarial and Financial Applications; Springer: London, 2013.
   Google Scholar
• Donnelly, C. Good-deal bounds in a regime switching market. Appl. Math. Opt. 2011, 18, 491–515.
   Google Scholar
• Donnelly, C.; Heunis, A.J., Quadratic risk minimization in a regime-switching with portfolio constraints. SIAM J. Control Opt. 2012, 50, 2431–2461.
   Web of Science ®Google Scholar
• Elliott, R.J.; Siu, T.K.; Chan, L.L.; Lau, J.W., Pricing options under a generalized Markov-modulated jump-diffusion model. Stoch Anal. Appl. 2007, 35, 694–713.
   Google Scholar
• Elliott, R.J.; Siu, T.K., On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy. Ann. Oper. Res. 2010, 176, 271–291.
   Web of Science ®Google Scholar
• Elliott, R.J.; Siu, T.K.; Badescu, A. On pricing and hedging options in regime-switching models with feedback effect. J. Econ. Dynamics Control 2011, 35, 694–713.
   Web of Science ®Google Scholar
• Hamilton, J.D., A new approach to the economic analysis of nonstationary time series and the business cycles. Econometrica 1989, 57, 357–384.
   Web of Science ®Google Scholar
• Hardy, M. A regime-switching model of long-term stock returns. N. Amer. Actuarial J. 2001, 52, 41–53.
   Google Scholar
• He, S.; Wang, J.; Yan, J. Semimartingale Theory and Stochastic Calculus; CRC Press: Beijing, 1992.
   Google Scholar
• Jacod, J.; Shiryaev, A.N., Limit Theorems for Stochastic Processes; Springer Verlag: Berlin, 2003.
   Google Scholar
• Leitner, J. Pricing and hedging with globally and instantaneously vanishing risk. Stat. Decisions 2007, 25, 311–332.
   Google Scholar
• Lo, A.W., The statistics of Sharpe ratios. Fin. Anal. J. 2002, 58, 36–52.
   Web of Science ®Google Scholar
• Mamon, R.S.; Elliott, R.J., Hidden Markov Models in Finance; Springer: New York, 2007.
   Google Scholar
• Pelsser, A. Pricing in incomplete markets. Research report 2011.
   Google Scholar
• Protter, P. Stochastic Integration and Differential Equations; Springer Verlag: Berlin, 2004.
   Google Scholar
• Royer, M. Backward stochastic differential equations with jumps and related non-linear expectations. Stoch. Proc. Appl. 2006, 116, 1358–1376.
   Web of Science ®Google Scholar
• Siu, T.K.; Erlein, C.; Mamon, R.S., The pricing of credit default swaps under a Markov-modulated Merton’s structural model. N. Amer. Actuarial J. 2008, 12, 19–46.
   Google Scholar
• Siu, T.K., A game theoretic approach to option valuation under Markovian regime-switching models. Ins. Math. Econ. 2012, 42, 1146–1158.
   Google Scholar
• Wu, H.; Li, Z. Multi-period mean-variance portfolio selection with regime switching and a stochastic cash flow. Ins. Math. Econ. 2012, 50, 371–384.
   Web of Science ®Google Scholar
• Young, V. Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio. Ins. Math. Econ. 2008, 42, 691–703.
   Web of Science ®Google Scholar