Solving high-dimensional optimal stopping problems using deep learning

Autor: Timo Welti, Sebastian D. Becker, Arnulf Jentzen, Patrick Cheridito
Jazyk: angličtina
Rok vydání: 2021
Předmět:
FOS: Computer and information sciences
Computer Science - Machine Learning
Mathematical optimization
Computer science
Computational Finance (q-fin.CP)
68T07
60G40
65C05
91G60
Context (language use)
High dimensional
curse of dimensionality
01 natural sciences
Machine Learning (cs.LG)
Computational Engineering
Finance
and Science (cs.CE)
FOS: Economics and business
010104 statistics & probability
Quantitative Finance - Computational Finance
Dimension (vector space)
0502 economics and business
FOS: Mathematics
Optimal stopping
0101 mathematics
Computer Science - Computational Engineering
Finance
and Science
option pricing
050208 finance
Stochastic process
business.industry
Applied Mathematics
Deep learning
Probability (math.PR)
05 social sciences
Bermudan option
deep learning
American option
financial derivative
optimal stopping
Valuation of options
Artificial intelligence
business
Mathematics - Probability
Curse of dimensionality
Zdroj: European Journal of Applied Mathematics, 32 (3)
ISSN: 0956-7925
1469-4425
Popis: Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to the number of underlying assets. High-dimensional optimal stopping problems are, however, notoriously difficult to solve due to the well-known curse of dimensionality. In this work, we propose an algorithm for solving such problems, which is based on deep learning and computes, in the context of early exercise option pricing, both approximations of an optimal exercise strategy and the price of the considered option. The proposed algorithm can also be applied to optimal stopping problems that arise in other areas where the underlying stochastic process can be efficiently simulated. We present numerical results for a large number of example problems, which include the pricing of many high-dimensional American and Bermudan options, such as Bermudan max-call options in up to 5000 dimensions. Most of the obtained results are compared to reference values computed by exploiting the specific problem design or, where available, to reference values from the literature. These numerical results suggest that the proposed algorithm is highly effective in the case of many underlyings, in terms of both accuracy and speed.
European Journal of Applied Mathematics, 32 (3)
ISSN:0956-7925
ISSN:1469-4425
Databáze: OpenAIRE
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