  Introduced in the late 90s, the passport option gives its holder the right to
trade in a market and receive any positive gain in the resulting traded account
at maturity. Pricing the option amounts to solving a stochastic control problem
that for $d>1$ risky assets remains an open problem. Even in a correlated
Black-Scholes (BS) market with $d=2$ risky assets, no optimal trading strategy
has been derived in closed form. In this paper, we derive a discrete-time
solution for multi-dimensional BS markets with uncorrelated assets. Moreover,
inspired by the success of deep reinforcement learning in, e.g., board games,
we propose two machine learning-powered approaches to pricing general options
on a portfolio value in general markets. These approaches prove to be
successful for pricing the passport option in one-dimensional and
multi-dimensional uncorrelated BS markets.
