Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning

Merton, R. C., 1969. Lifetime portfolio selection under uncertainty: The continuous-time case. The Review of Economics and Statistics, 247–257

1969

Earlier work this paper cites.

Merton, R., 1971. Optimum consumption and portfolio-rules in a continuous-time framework. Journal of Economic Theory

1971

Earlier work this paper cites.

Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81 (3), 637–654

1973

Earlier work this paper cites.

Cybenko, G., 1989. Approximation by superpositions of a sigmoidal function. Mathematics of control, signals and systems 2 (4), 303–314

1989

Earlier work this paper cites.

Hornik, K., 1991. Approximation capabilities of multilayer feedforward networks. Neural networks 4 (2), 251–257

1991

Earlier work this paper cites.

Hochreiter, S., Schmidhuber, J., 1997. Long short-term memory. Neural computation 9 (8), 1735–1780

1997

Earlier work this paper cites.

Almgren, R., Chriss, N., 2001. Optimal execution of portfolio transactions. Journal of Risk 3, 5–40

2001

Earlier work this paper cites.

Burden, R. L., Faires, J. D., Reynolds, A. C., 2001. Numerical analysis. Brooks/cole Pacific Grove, CA

2001

Earlier work this paper cites.

Henderson, V., Hobson, D., 2002. Substitute hedging. Risk Magazine 15 (5), 71–76

2002

Earlier work this paper cites.

Henderson, V., Hobson, D., 2004. Utility indifference pricing: An overview. Volume on Indifference Pricing

2004

Earlier work this paper cites.

Achdou, Y., Pironneau, O., 2005. Computational methods for option pricing. Vol. 30. Siam

2005

Cited alongside, same era.

Bishop, C. M., 2006. Pattern Recognition and Machine Learning. Springer

2006

Cited alongside, same era.

Huang, M., Malhamé, R. P., Caines, P. E., 2006. Large population stochastic dynamic games: closed-loop Mckean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6 (3), 221–252

2006

Cited alongside, same era.

Lasry, J.-M., Lions, P.-L., 2007. Mean field games. Japanese Journal of Mathematics 2 (1), 229–260

2007

Cited alongside, same era.

Pham, H., 2009. Continuous-Time Stochastic Control and Optimization with Financial Applications. Vol. 61. Springer Science & Business Media

2009

Cited alongside, same era.

Shalev-Shwartz, S., Ben-David, S., 2014. Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press

2014

Later among the works it cites.

Carmona, R., Sun, L.-H., Fouque, J.-P., 2015. Mean field games and systemic risk. Communications in Mathematical Sciences 14 (4), 911–933

2015

Later among the works it cites.

Cartea, Á., Jaimungal, S., 2015. Optimal execution with limit and market orders. Quantitative Finance 15 (8), 1279–1291

2015

Later among the works it cites.

Cartea, Á., Jaimungal, S., Penalva, J., 2015. Algorithmic and high-frequency trading. Cambridge University Press

2015

Later among the works it cites.

Srivastava, R. K., Greff, K., Schmidhuber, J., 2015. Highway networks. arXiv preprint arXiv:1505.00387

Original

2015

Later among the works it cites.