  This article presents a deep reinforcement learning approach to price and
hedge financial derivatives. This approach extends the work of Guo and Zhu
(2017) who recently introduced the equal risk pricing framework, where the
price of a contingent claim is determined by equating the optimally hedged
residual risk exposure associated respectively with the long and short
positions in the derivative. Modifications to the latter scheme are considered
to circumvent theoretical pitfalls associated with the original approach.
Derivative prices obtained through this modified approach are shown to be
arbitrage-free. The current paper also presents a general and tractable
implementation for the equal risk pricing framework inspired by the deep
hedging algorithm of Buehler et al. (2019). An $\epsilon$-completeness measure
allowing for the quantification of the residual hedging risk associated with a
derivative is also proposed. The latter measure generalizes the one presented
in Bertsimas et al. (2001) based on the quadratic penalty. Monte Carlo
simulations are performed under a large variety of market dynamics to
demonstrate the practicability of our approach, to perform benchmarking with
respect to traditional methods and to conduct sensitivity analyses.
