analytical approximation for the American Option pricing by fitting the empirical function to the results of the American put option prices generated by BOPM. Following a different approach, if the underlying asset is modeled as the Markov Process, the Bellman principle of Dynamic Programming (DP) [5] can be used to compute the option value. However, this approach becomes impractical when the state space has many dimensions since the DP algorithm requires an exponential memory space in the number of dimensions. This problem is known as the \"curse of dimensionality\" for DP. To overcome this problem, ref. [6] proposed that the state space domain was partitioned into a finite number of regions, and the continuation value was approximated. Similarly, Least Squares Monte Carlo (LSM) method was proposed to approximate the continuation value with regression on a set of basis functions to develop a low-dimensional approximation to the expected continuation value [7]. Since the optimal exercise time of the American Option is a Sequential Decision-Making problem, with two possible actions at each time step, the Reinforcement Learning (RL) [8] approach has been used to find the fair value of option price by learning the optimal policy. Reinforcement learning (RL) is a model-free approach for Sequential Decision-Making, where explicit modeling of the environment (quantifying uncertainty) is no longer needed. The initial significant contribution to the field of RL was the advent of Q-Learning by [9]. Further, the integration of the RL algorithm and neural networks led to the development of Deep Reinforcement Learning (DRL), particularly with the introduction of the Deep Q-Network (DQN) [10], enabling RL to be applied to more complex tasks like Atari games using deep convolutional neural networks for approximating Q value function in them. Later developments, such as Proximal Policy Optimization (PPO) by [11] and Soft Actor-Critic (SAC) by [12], further advanced the field of RL by introducing policy gradient methods as a new form of finding an optimal policy in Sequential Decision-Making. More recently, model-based RL like DreamerV2 [13] that learn policy through building the latent space of the world model has improved the sample efficiency of the method. Multi-task Reinforcement Learning [14] has also enhanced the scalability and data efficiency of RL methods. Least Squares Policy Iteration (LSPI) was proposed to learn the optimal policy for pricing the American Option [15]. They considered both Geometric Brownian Motion (GBM) and a stochastic volatility model as the underlying asset price models and showed good quality of the policy learned by RL. The work of [16] employed a deep learning method to learn the optimal stopping times from Monte Carlo samples. They showed that the resulting stopping policy (neural network policy) can approximate the optimal stopping times. Iteration algorithm for pricing American Options based on Reinforcement Learning was proposed in [17]. At each iteration, the method approximates the expected discounted payoff of stopping times and produces those closer to optimal. A thorough literature review of the modeling and pricing of the American Option (both classical and RL-based methods) can be found in [18]. Reinforcement learning has also been applied to dynamic stock option hedging in markets calibrated with stochastic volatility models [19]. A comprehensive review of the application of Reinforcement Learning for option hedging, as well as recent advances in utilizing Reinforcement Learning for various decision-making processes in finance, can be found in [20; 21].