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The optimal stopping problem is a category of decision problems with aspecific constrained configuration. It is relevant to various real-worldapplications such as finance and management. To solve the optimal stoppingproblem, state-of-the-art algorithms in dynamic programming, such as theleast-squares Monte Carlo (LSMC), are employed. This type of algorithm relieson path simulations using only the last price of the underlying asset as astate representation. Also, the LSMC was thinking for option valuation whererisk-neutral probabilities can be employed to account for uncertainty. However,the general optimal stopping problem goals may not fit the requirements of theLSMC showing auto-correlated prices. We employ a data-driven method that usesMonte Carlo simulation to train and test artificial neural networks (ANN) tosolve the optimal stopping problem. Using ANN to solve decision problems is notentirely new. We propose a different architecture that uses convolutionalneural networks (CNN) to deal with the dimensionality problem that arises whenwe transform the whole history of prices into a Markovian state. We presentexperiments that indicate that our proposed architecture improves results overthe previous implementations under specific simulated time series functionsets. Lastly, we employ our proposed method to compare the optimal exercise ofthe financial options problem with the LSMC algorithm. Our experiments showthat our method can capture more accurate exercise opportunities when comparedto the LSMC. We have outstandingly higher (above 974\% improvement) expectedpayoff from these exercise policies under the many Monte Carlo simulations thatused the real-world return database on the out-of-sample (test) data.

Solving the optimal stopping problem with reinforcement learning: an application in financial option exercise