Phương pháp sai phân hữu hạn cho các phương trình Hamilton-Jacobi-Bellman phát sinh trong tối ưu hóa tiện ích chuyển đổi chế độ
Tóm tắt
Từ khóa
#Tối ưu hóa tiện ích #phương trình Hamilton-Jacobi-Bellman #phương pháp sai phân hữu hạn #chuyển đổi chế độ #hội tụTài liệu tham khảo
Azimzadeh, P., Forsyth, P.: Weakly chained matrices and impulse control. SIAM J. Numer. Anal. 54, 1341–1364 (2016)
Babbin, J., Forsyth, P., Labahn, G.: A comparison of iterated optimal stopping and local policy iteration for American options under regime switching. J. Sci. Comput. 58, 409–430 (2014)
Barles, G.: Convergence of numercial schemes for degenerate parabolic equations arising in finance. In: Rogers, L., Talay, D. (eds.) Numerical Methods in Finance, pp. 1–21. Cambridge University Press, Cambridge (1997)
Barles, G., Souganidis, P.: Convergence of approximation schemes for fully nonlinear second order equations. Asympt. Anal. 4, 271–283 (1991)
Bäuerle, N., Rieder, U.: Portfolio optimization with Markov-modulated stock prices and interest rates. IEEE Trans. Autom. Control 29, 442–447 (2005)
Bian, B., Miao, S., Zheng, H.: Smooth value functions for a class of nonsmooth utility maximization problems. SIAM J. Financ. Math. 2, 727–747 (2011)
Bian, B., Zheng, H.: Turnpike property and convergence rate for an investment model with general utility functions. J. Econ. Dyn. Control 51, 28–49 (2015)
Buffington, J., Elliott, R.: Regime switching and European options. Stochast. Theory Control 280, 73–82 (2002)
Canakog̈lu, E., Özekici, S.: HARA frontiers of optimal portfolios in stochastic markets. Eur. J. Oper. Res. 221, 129–137 (2012)
Dang, D., Forsyth, P.: Better than pre-commitment mean-variance portfolio allocation strategies a semi-self-financing Hamilton–Jacobi–Bellman equation approach. Eur. J. Oper. Res. 250, 827–841 (2016)
Forsyth, P.: A Hamilton–Jacobi–Bellman approach to optimal trade execution. Appl. Numer. Math. 61, 241–265 (2011)
Forsyth, P., Kennedy, J., Tse, T., Windcliff, H.: Optimal trade execution: a mean quadratic variation approach. J. Econ. Dyn. Control 36, 1971–1991 (2012)
Forsyth, P., Labahn, G.: Numerical methods for controlled Hamilton–Jacobi–Bellman PDEs in finance. J. Comput. Finance 11, 1–44 (2008)
Forsyth, P., Labahn, G.: \(\varepsilon \)-monotone Fourier methods for optimal stochastic control in finance. J. Comput. Finance 22, 25–71 (2019)
Forsyth, P., Ma, K.: Numerical solution of the Hamilton–Jacobi–Bellman formulation for continuous-time mean-variance asset allocation under stochastic volatility. J. Comput. Finance 20, 1–37 (2016)
Fu, J., Wei, J., Yang, H.: Portfolio optimization in a regime-switching market with derivatives. Eur. J. Oper. Res. 233, 184–192 (2014)
Hamilton, J.: A new approach to the economic analysis of nonstationary time series and the business cycle. Ecomometrica 57, 357–384 (1989)
Hardy, M.: A regime-switching model for long-term stock returns. North Am. Actuarial J. 5, 41–53 (2001)
Honda, T.: Optimal portfolio choice for unobservable and regime-switching mean returns. J. Econ. Dyn. Control 28, 45–78 (2003)
Huang, Y., Forsyth, P., Labahn, G.: Methods for pricing American options under regime switching. SIAM J. Sci. Comput. 33, 2144–2168 (2011)
Huang, Y., Forsyth, P., Labahn, G.: Combined fixed point and policy iteration for HJB equations in finance. SIAM J. Numer. Anal. 50, 1849–1860 (2012)
Li, H., Mollapourasl, R., Haghi, M.: A local radial basis function method for pricing options under the regime switching model. J. Sci. Comput. 79, 517–541 (2019)
Ma, J., Li, W., Zheng, H.: Dual control Monte-Carlo method for tight bounds of value function in regime switching utility maximization. Eur. J. Oper. Res. 263, 851–862 (2017)
Mollapourasl, R., Haghi, M., Liu, R.: Localized kernel-based approximation for pricing financial options under regime switching jump diffusion model. Appl. Numer. Math. 134, 81–104 (2018)
Pham, H.: Continuous-Time Stochastic Control and Optimization with Financial Applications. Springer, New York (2009)
Pooley, D., Forsyth, P., Vetzal, K.: Numerical convergence properties of option pricing PDEs with uncertain volatility. IMA J. Numer. Anal. 23, 241–267 (2003)
Reisinger, C., Forsyth, P.: Piecewise constant policy approximations to Hamilton–Jacobi–Bellman equations. Appl. Numer. Math. 103, 27–47 (2016)
Rieder, U., Bäuerle, N.: Portfolio optimization with unobservable Markov-modulated drift process. J. Appl. Prob. 43, 362–378 (2005)
Sass, J., Haussmann, U.: Optimizing the terminal wealth under partial information: the drift process as a continuous time Markov chain. Finance Stochast. 8, 553–577 (2004)
Tse, T., Forsyth, P., Kennedy, J., Windcliff, H.: Comparison between the mean variance optimal and mean quadratic variation optimal trading strategies. Appl. Math. Finance 20, 415–449 (2013)
Wang, J., Forsyth, P.: Numerical solution of the Hamilton–Jacobi–Bellman formulation for continuous time mean variance asset allocation. J. Econ. Dyn. Control 34, 207–230 (2010)
Yao, D., Zhang, Q., Zhou, X.: A Regime-Switching Model for European Option Pricing. Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering. Springer, New York (2006)
Yin, G., Zhang, Q., Liu, F., Liu, R., Cheng, Y.: Stock liquidation via stochastic approximation using NASDAQ daily and intra-day data. Math. Finance 16, 217–236 (2006)
Yong, J., Zhou, X.: Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer, New York (1999)
Zhang, Q., Yin, G., Liu, R.: A near-optimal selling rule for a two-time-scale market model. SIAM J. Multiscale Model. Simul. 4, 172–193 (2005)
Zhou, X., Yin, G.: Markowitz’s mean-variance portfolio selection with regime switching: a continuous-time model. SIAM J. Control Optim. 42, 1466–1482 (2003)