Numerical solving of the generalized Black-Scholes differential equation using Laguerre neural network
Tài liệu tham khảo
Alziary, 1997, A P.D.E. approach to Asian options: analytical and numerical evidence, J. Bank. Finance, 21, 613, 10.1016/S0378-4266(96)00057-X
Amster, 2005, A Black–Scholes option pricing model with transaction costs, J. Math. Anal. Appl., 303, 688, 10.1016/j.jmaa.2004.08.067
Anitescu, 2019, Artificial neural network methods for the solution of second order boundary value problems, Comput. Mater. Continua, 59, 345, 10.32604/cmc.2019.06641
Ankudinova, 2008, On the numerical solution of nonlinear Black–Scholes equations, Comput. Math. Appl., 56, 799, 10.1016/j.camwa.2008.02.005
Arenas, 2013, A nonstandard finite difference scheme for a nonlinear Black–Scholes equation, Math. Comput. Model., 57, 1663, 10.1016/j.mcm.2011.11.009
Black, 1973, The pricing of options and corporate liabilities, J. Polit. Econ., 81, 637, 10.1086/260062
Chan, 1999, Pricing contingent claims on stocks driven by Levy processes, Ann. Appl. Probab., 9, 504, 10.1214/aoap/1029962753
Chen, 2020, A deep residual compensation extreme learning machine and applications, J. Forecast., 10.1002/for.2663
Company, 2006, Numerical solution of modified Black–Scholes equation pricing stock options with discrete dividend, Math. Comput. Model., 44, 1058, 10.1016/j.mcm.2006.03.009
Cox, 1979, Option pricing: a simplified approach, J. Financ. Econ., 7, 229, 10.1016/0304-405X(79)90015-1
Cui, 2020, Predicting product return volume using machine learning methods, Eur. J. Oper. Res., 281, 612, 10.1016/j.ejor.2019.05.046
Dufresne, 2000, Laguerre series for Asian and other options, Math. Finance, 10, 407, 10.1111/1467-9965.00101
Forsyth, 1999, A finite element approach to the pricing of discrete lookbacks with stochastic volatility, Appl. Math. Finance, 6, 87, 10.1080/135048699334564
Fu, 2000, A note on perturbation analysis estimators for American-style options, Probab. Eng. Inf. Sci., 14, 385, 10.1017/S0269964800143086
Godin, 2019, Option pricing under regime-switching models: novel approaches removing path-dependence, Insur. Math. Econ., 87, 130, 10.1016/j.insmatheco.2019.04.006
Hansen, 2000, Analytical valuation of American-style Asian options, Manag. Sci., 46, 1116, 10.1287/mnsc.46.8.1116.12027
Hou, 2018, Forecasting time series with optimal neural networks using multi-objective optimization algorithm based on AICc, Front. Comput. Sci., 12, 1261, 10.1007/s11704-018-8095-8
Huang, 2010, Optimization method based extreme learning machine for classification, Neurocomputing, 74, 155, 10.1016/j.neucom.2010.02.019
Huang, 2006, Extreme learning machine: theory and applications, Neurocomputing, 70, 489, 10.1016/j.neucom.2005.12.126
Huang, 2004, Extreme learning machine: a new learning scheme of feedforward neural networks, 985
Huang, 2017
Jarrow, 1999, A partial differential equation that changed the world, J. Econ. Perspect., 13, 229, 10.1257/jep.13.4.229
Kangro, 2000, Far field boundary conditions for Black-Scholes equations, SIAM J. Numer. Anal., 38, 1357, 10.1137/S0036142999355921
Khabir, 2012, Spline approximation method to solve an option pricing problem, J. Differ. Equ. Appl., 18, 1801, 10.1080/10236198.2011.596150
Kim, 2020, Can deep learning predict risky retail investors? A case study in financial risk behavior forecasting, Eur. J. Oper. Res., 283, 217, 10.1016/j.ejor.2019.11.007
Kulaglic, 2018, Stock price forecast using wavelet transformations in multiple time windows and neural networks, 518
Lam, 2002
Leigh, 2002, Forecasting the NYSE composite index with technical analysis, pattern recognizer, neural network, and genetic algorithm: a case study in romantic decision support, Decis. Support Syst., 32, 361, 10.1016/S0167-9236(01)00121-X
Lu, 2020, Solving the ruin probabilities of some risk models with Legendre neural network algorithm, Digit. Signal Process., 99, 10.1016/j.dsp.2019.102634
Lu, 2019, The LS-SVM algorithms for boundary value problems of high-order ordinary differential equations, Adv. Differ. Equ.
Mall, 2017, Single layer Chebyshev neural network model for solving elliptic partial differential equations, Neural Process. Lett., 45, 825, 10.1007/s11063-016-9551-9
Marco, 1994, Dynamic hedging portfolios for derivative securities in the presence of large transaction costs, Appl. Math. Finance, 1, 165, 10.1080/13504869400000010
Markowitz, 1952, Portfolio selection*, J. Finance, 7, 77
Martinez, 2020, A machine learning framework for customer purchase prediction in the non-contractual setting, Eur. J. Oper. Res., 281, 588, 10.1016/j.ejor.2018.04.034
Menkveld, 2000, A pricing model for American options with Gaussian interest rates, Ann. Oper. Res., 100, 211, 10.1023/A:1019275302878
Merton, 1973, Rational theory of option pricing, Bell J. Econ., 4, 141, 10.2307/3003143
Merton, 1974, On the pricing of corporate debt: the risk structure of interest rates*, J. Finance, 29, 449
Merton, 1976, Option prices when underlying stock returns are discontinuous, J. Financ. Econ., 3, 125, 10.1016/0304-405X(76)90022-2
Michalak, 2005, Prediction of high increases in stock prices using neural networks, Neural Netw. World, 15, 359
Ozdemir, 2017, Numerical solution of fractional Black-Scholes equation by using the multivariate Pade approximation, Acta Phys. Pol. A, 132, 1050, 10.12693/APhysPolA.132.1050
Pakdaman, 2017, Solving differential equations of fractional order using an optimization technique based on training artificial neural network, Appl. Math. Comput., 293, 81, 10.1016/j.amc.2016.07.021
Qu, 2015, A numerical method for solving fractional differential equations by using neural network, Adv. Math. Phys., 2015, 10.1155/2015/439526
Refenes, 1997, Neural networks in financial engineering: a study in methodology, IEEE Trans. Neural Netw., 8, 1222, 10.1109/72.641449
Rhim, 2000, An estimation of early exercise premium for American put options, Glob. Bus. Finance Rev., 5, 13
Rikukawa, 2020, Recurrent neural network based stock price prediction using multiple stock brands, Int. J. Innov. Comput. Inf. Control, 16, 1093
Rizaner, 2018, Approximate solutions of initial value problems for ordinary differential equations using radial basis function networks, Neural Process. Lett., 48, 1063, 10.1007/s11063-017-9761-9
Roul, 2019, A high order numerical method and its convergence for time-fractional fourth-order partial differential equations, Appl. Math. Comput., 366
Roul, 2020, A new higher order compact finite difference method for generalised Black-Scholes partial differential equation: European call option, J. Comput. Appl. Math., 363, 464, 10.1016/j.cam.2019.06.015
Sen Tan, 2018, Solving ordinary differential equations using neural networks
Simon, 2000, An easy computable upper bound for the price of an arithmetic Asian option, Insur. Math. Econ., 26, 175, 10.1016/S0167-6687(99)00051-7
Sun, 2019, Solving partial differential equation based on Bernstein neural network and extreme learning machine algorithm, Neural Process. Lett., 50, 1153, 10.1007/s11063-018-9911-8
Touzi, 1999, American options exercise boundary when the volatility changes randomly, Appl. Math. Optim., 39, 411, 10.1007/s002459900112
Wang, 2018, A study on the stock market prediction based on genetic neural network, 105
Wang, 2011, Forecasting stock indices with back propagation neural network, Expert Syst. Appl., 38, 14346, 10.1016/j.eswa.2011.04.222
Wang, 2020, An effective CNN method for fully automated segmenting subcutaneous and visceral adipose tissue on CT scans, Ann. Biomed. Eng., 48, 312, 10.1007/s10439-019-02349-3
Wang, 2021, Automatically discriminating and localizing COVID-19 from community-acquired pneumonia on chest X-rays, Pattern Recognit., 110, 10.1016/j.patcog.2020.107613
Wu, 2017, A performance comparison of neural networks in forecasting stock price trend, Int. J. Comput. Intell. Syst., 10, 336, 10.2991/ijcis.2017.10.1.23
Xi, 2014, A new constructive neural network method for noise processing and its application on stock market prediction, Appl. Soft Comput., 15, 57, 10.1016/j.asoc.2013.10.013
Yakuwa, 2003, Novel time series analysis and prediction of stock trading using fractal theory and time delayed neural network, 134
Yang, 2018, A novel improved extreme learning machine algorithm in solving ordinary differential equations by Legendre neural network methods, Adv. Differ. Equ., 10.1186/s13662-018-1927-x
Yang, 2020, Numerical solution of several kinds of differential equations using block neural network method with improved extreme learning machine algorithm, J. Intell. Fuzzy Syst., 38, 3445, 10.3233/JIFS-190406
Yang, 2020, Neural network algorithm based on Legendre improved extreme learning machine for solving elliptic partial differential equations, Soft Comput., 24, 1083, 10.1007/s00500-019-03944-1
Yavuz, 2020, European option pricing models described by fractional operators with classical and generalized Mittag-Leffler kernels, Numer. Methods Partial Differ. Equ., 10.1002/num.22645
Yavuz, 2018, A different approach to the European option pricing model with new fractional operator, Math. Model. Nat. Phenom., 13, 10.1051/mmnp/2018009
Yavuz, 2018, European vanilla option pricing model of fractional order without singular kernel, Fractal Fract., 2, 10.3390/fractalfract2010003
Yavuz, 2018
Yavuz, 2016
Yinghao, 2020, Solution of ruin probability for continuous time model based on block trigonometric exponential neural network, Symmetry, 12, 876, 10.3390/sym12060876
Zhou, 2019, Numerical solution for ruin probability of continuous time model based on neural network algorithm, Neurocomputing, 331, 67, 10.1016/j.neucom.2018.08.020