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What Next?

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Mathematics Going Forward

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2313))

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Abstract

Developments of computing power, but more particularly of easy-to-use packages for statistics, symbolic mathematics, PDE solving, … have hugely expanded the scope of what the mathematical sciences can now tackle, and we have to seize the opportunities this opens up.

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References

  1. L. Andersen and M. Broadie. Primal-dual simulation algorithm for pricing multidimensional American options. Management Science50(9), 1222–1234 (2004).

    Article  Google Scholar 

  2. S. Becker, P. Cheridito and A. Jentzen. Deep optimal stopping. Journal of Machine Learning Research20, 74 (2019).

    MathSciNet  MATH  Google Scholar 

  3. R.E. Bellman. The theory of dynamic programming. Bulletin of the American Mathematical Society60(6), 503–515 (1954).

    Article  MathSciNet  MATH  Google Scholar 

  4. M.H.A. Davis and I. Karatzas. A deterministic approach to optimal stopping. In: Probability, Statistics and Optimisation (ed. F. P. Kelly), pp. 455–466, New York Chichester: John Wiley & Sons Ltd (1994).

    Google Scholar 

  5. J. Han and W. E. Deep learning approximation for stochastic control problems. arXiv preprint arXiv:1611.07422 (2016).

    Google Scholar 

  6. M.B. Haugh and L. Kogan. Pricing American options: a duality ap- proach. Operations Research52(2), 258–270 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  7. L.C.G. Rogers. Monte Carlo valuation of American options. Mathematical Finance12(3), 271–286 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  8. L.C.G. Rogers. Pathwise stochastic optimal control. SIAM Journal on Control and Optimization46(3), 1116–1132 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  9. G.N. Watson. A treatise on the theory of Bessel functions. Cambridge University Press (1995).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Statistical Laboratory, University of Cambridge, Cambridge, UK

    L. C. G. Rogers

Authors
  1. L. C. G. Rogers
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Correspondence to L. C. G. Rogers .

Editor information

Editors and Affiliations

  1. CMLA, École Normale Supérieure, Cachan CX, France

    Jean-Michel Morel

  2. Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013, Paris, France

    Bernard Teissier

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Rogers, L.C.G. (2023). What Next?. In: Morel, JM., Teissier, B. (eds) Mathematics Going Forward . Lecture Notes in Mathematics, vol 2313. Springer, Cham. https://doi.org/10.1007/978-3-031-12244-6_8

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