  The QLBS model is a discrete-time option hedging and pricing model that is
based on Dynamic Programming (DP) and Reinforcement Learning (RL). It combines
the famous Q-Learning method for RL with the Black-Scholes (-Merton) model's
idea of reducing the problem of option pricing and hedging to the problem of
optimal rebalancing of a dynamic replicating portfolio for the option, which is
made of a stock and cash. Here we expand on several NuQLear (Numerical
Q-Learning) topics with the QLBS model. First, we investigate the performance
of Fitted Q Iteration for a RL (data-driven) solution to the model, and
benchmark it versus a DP (model-based) solution, as well as versus the BSM
model. Second, we develop an Inverse Reinforcement Learning (IRL) setting for
the model, where we only observe prices and actions (re-hedges) taken by a
trader, but not rewards. Third, we outline how the QLBS model can be used for
pricing portfolios of options, rather than a single option in isolation, thus
providing its own, data-driven and model independent solution to the (in)famous
volatility smile problem of the Black-Scholes model.
