Optimal Redeeming Strategy of Stock Loans Under Drift Uncertainty

References

• [1] Bain A, Crisan D (2009) Fundamentals of Stochastic Filtering, Stochastic Modelling and Applied Probability, vol. 60 (Springer, New York).Crossref, Google Scholar
• [2] Cai N, Sun L (2014) Valuation of stock loans with jump risk. J. Econom. Dynam. Control 40(3):213–241.Crossref, Google Scholar
• [3] Chen X, Yi F, Wang L (2011) American lookback option with fixed strike price—2D parabolic variational inequality. J. Differential Equations 251(11):3063–3089.Crossref, Google Scholar
• [4] Dai M, Xu ZQ (2011) Optimal redeeming strategy of stock loans with finite maturity. Math. Finance 21(4):775–793.Google Scholar
• [5] Dai M, Zhong YF (2012) Optimal stock selling/buying strategy with reference to the ultimate average. Math. Finance 22(1):165–184.Crossref, Google Scholar
• [6] Dai M, Zhang Q, Zhu QJ (2010) Trend following trading under a regime switching model. SIAM J. Financial Math. 1(1):780–810.Crossref, Google Scholar
• [7] Dai M, Zhou Y, Zhong YF (2012) Optimal stock selling based on the global maximum. SIAM J. Control Optim. 50(4):1804–1822.Crossref, Google Scholar
• [8] Dai M, Jin H, Zhong YF, Zhou XY (2010) Buy low and sell high. Chiarella C, Novikov A, eds. Contemporary Quantitative Finance (Springer, Berlin), 317–333.Google Scholar
• [9] Décamps JP, Mariotti T, Villeneuve S (2005) Investment timing under incomplete information. Math. Oper. Res. 30(2):472–500.Link, Google Scholar
• [10] Detemple J, Tian W, Xiong J (2012) Optimal stopping with reward constraints. Finance Stochastics 16(3):423–448.Crossref, Google Scholar
• [11] Ekstr E, Vaicenavicius J (2015) Optimal liquidation of an asset under drift uncertainty. SIAM J. Financial Math. 7(1):357–381.Crossref, Google Scholar
• [12] Friedman A (1982) Variational Principles and Free Boundary Problems (John Wiley & Sons, New York).Google Scholar
• [13] Guo X (2001) Inside information and option pricings. Quant. Finance 1(1):38–44.Crossref, Google Scholar
• [14] Guo X (2001) An explicit solution to an optimal stopping problem with regime switching. J. Appl. Probab. 38(2):464–481.Crossref, Google Scholar
• [15] Kallianpur G, Xiong J (2001) Asset pricing with stochastic volatility. Appl. Math. Optim. 43(1):47–62.Crossref, Google Scholar
• [16] Lamberton D, Zervos M (2013) On the optimal stopping of a one-dimensional diffusion. Electronic J. Probab. 18:34–49.Crossref, Google Scholar
• [17] Leung T, Li X, Wang Z (2015) Optimal multiple trading times under the exponential OU model with transaction costs. J. Stochastic Models 31(4):554–587.Crossref, Google Scholar
• [18] Li X, Tan HH, Wilson C, Wu ZY (2013) When should venture capitalists exit their investee companies? Internat. J. Management Finance 9(4):351–364.Google Scholar
• [19] Liang Z, Nie Y, Zhao L (2012) Valuation of infinite maturity stock loans with geometric Levy model in a risk-neutral framework. Working paper, Tsinghua University, Beijing, https://pdfs.semanticscholar.org/7cd2/7b51fc509822ec02e130bc93fc7cd86f8396.pdf.Google Scholar
• [20] Liptser R, Shiryaev AN (2001) Statistics of Random Processes, I. General Theory (Springer, Berlin).Google Scholar
• [21] Oleinik OA, Radkevie EV (1973) Second Order Equations with Nonnegative Characteristic Form (Plenum Press, New York).Crossref, Google Scholar
• [22] Pham H (2009) Continuous-Time Stochastic Control and Optimization with Financial Applications, Stochastic Modelling and Applied Probability, vol. 61 (Springer, Berlin).Crossref, Google Scholar
• [23] Prager D, Zhang Q (2010) Stock loan valuation under a regime-switching model with mean-reverting and finite maturity. J. Systems Sci. Complex 23(3):572–583.Crossref, Google Scholar
• [24] Shiryaev AN (2008) Optimal Stopping Rules (Springer, Berlin).Google Scholar
• [25] Shiryaev AN (2009) On stochastic models and optimal methods in the quickest detection problems. Theory Probab. Appl. 53(3):385–401.Crossref, Google Scholar
• [26] Shiryaev AN, Novikov AA (2008) On a stochastic version of the trading rule “buy and hold.” Statist. Decisions 26:289–302.Google Scholar
• [27] Shiryaev AN, Xu ZQ, Zhou XY (2008) Thou shalt buy and hold. Quant. Finance 8(8):765–776.Crossref, Google Scholar
• [28] Shiryaev AN, Zhitlukhin MV, Ziemba WT (2014) When to sell Apple and the NASDAQ? Trading bubbles with a stochastic disorder model. J. Portfolio Management 40(2):54–63.Crossref, Google Scholar
• [29] Song QS, Yin G, Zhang Q (2009) Stochastic optimization methods for buying-low-and-selling-high strategies. Stochastic Anal. Appl. 27(3):523–542.Crossref, Google Scholar
• [30] Vannestå l M (2017) Optimal timing decisions in financial markets. Doctoral thesis, Uppsala University, Uppsala, Sweden.Google Scholar
• [31] Xia J, Zhou XY (2007) Stock loans. Math. Finance 17(2):307–317.Crossref, Google Scholar
• [32] Xiong J (2008) An Introduction to Stochastic Filtering Theory (Oxford University Press, New York).Google Scholar
• [33] Xiong J, Zhou XY (2007) Mean–variance portfolio selection under partial information. SIAM J. Control Optim. 46(1):156–175.Crossref, Google Scholar
• [34] Xu ZQ (2016) A note on the quantile formulation. Math. Finance 26(3):589–601.Crossref, Google Scholar
• [35] Xu ZQ, Zhou XY (2013) Optimal stopping under probability distortion. Ann. Appl. Probab. 23(1):251–282.Crossref, Google Scholar
• [36] Yong JM, Zhou XY (1999) Stochastic Controls Hamiltonian Systems and HJB Equations (Springer, New York).Google Scholar
• [37] Zervos M, Johnson T, Alazemi F (2012) Buy-low and sell-high investment strategies. Math. Finance 23(3):560–578.Crossref, Google Scholar
• [38] Zhang Q (2001) Stock trading: An optimal selling rule. SIAM J. Control Optim. 40(1):64–87.Crossref, Google Scholar
• [39] Zhang Q, Zhou XY (2009) Valuation of stock loans with regime switching. SIAM J. Control Optim. 48(3):1229–1250.Crossref, Google Scholar
• [40] Zhitlukhin MV, Shiryaev AN (2013) Baeyes disorder problems on filtered probability spaces. Theory Probab. Appl. 57(3):497–511.Crossref, Google Scholar
• [41] Zhitlukhin MV, Shiryaev AN (2014) Optimal stopping problems for a Brownian motion with disorder on a segment. Theory Probab. Appl. 58(1):164–171.Crossref, Google Scholar