The popularity of deep reinforcement learning (DRL) methods in economics have been exponentially increased. DRL , through a wide range of capabilities from reinforcement learning (RL) to deep learning (DL) , offers vast opportunities for handling sophisticated economics dynamic systems. DRL is characterized by scalability with the potential to be applied to high -dimensional problems in conjunction with noisy and nonlinear patterns of economic data. In this paper , we initially consider a brief review of DL, RL, and deep RL methods in diverse appl ications in economics , providing an in -depth insight into state of the art. Furthermore, the architecture of DRL applied to economic applications is investigated in order to highlight the complexity, robustness, accuracy, performance, computational tasks, risk constraints, and profitability. The survey results indicate that DRL can provide better performance and higher efficien cy as compared to the traditional algorithms while facing real economic problems at the presence of risk parameters and the ever -increasing uncertainties. Keywords: Economic s; deep reinforcement learning; deep learning; machine learning 1. Introductio n Deep learning (DL) techniques are based on the usage of multi -neuron that rely on the multi -layer architectures to accomplish a learning task. In DL, the neurons are linked to the input data in conjunction with loss function for the purpose of updating its weights and of maximizing the fitting to the i nbound data [1, 2] . In the structure of a multi -layer, every node takes the outputs of all the prior layers in order to represent outputs set b y diminishing the approximation of the primary input data , while multiple -neurons perform to learn various weights on the same data at the same time. There is a great demand for the appropriate mechanisms to improv e productivity and product quality in the current market development. Deep learning enable s predict ing and investigate complicated market trend s compared to the traditional algorithms in ML. DL presents great potential to provide powerful tools to learn from stochastic data arising from multiple sources that can 2 of 45 efficiently extract complicated relationships and features from the given data . DL reported to present efficient predictive tool s to analyze the market [3, 4] . Additionally, compared to the traditional algorithms, DL is able to prevent the over -fitting problem, to provi de more efficient sample fitting associated with complicated interactions, and to outstretch input data to cover all the essential feature s of the relevant problem [5]. Reinforcement Learning (RL) [6] is a powerful mathematical framework for experience -driven autonomous learning [7]. In RL, the agents interact directly with the environment by taking actions to enhance its efficiency by trial -and-error to optimize the cumulative reward without requiring labeled data. Policy search and value function approximation ar e critical tools of autonomous learning . The search policy of RL is to detect an optimal (stochastic) policy applying gradient -based or gradient -free approaches dealing with both continuous and discrete state -action settings [8]. The value function strategy is to estimate the expected return in order to find the optimal policy dealing with all possible actions based on the given state. While considering an economic problem, despite traditional approaches [9], reinforcement learning methods prevent suboptimal performance, namely by imposing significant market constraints that lead to finding optimal strategy in terms of market analysis and forecast [10]. Despite RL successes in recent years [11-13], these results suffer the lack of scalability and disable to manage high dimensional problems. DRL technique by combining both RL and DL methods where DL equipped with the vigorous function approximation, representation learning properties of deep neural networks (DNN) , and handling complex and nonlinear patterns of economic data can efficiently overcome these problems [14] [15]. Ultima tely, the purpose of this paper is to comprehensively give an overview of the state -of-the-art in the application of both deep learning (DL) and deep reinforcement learning (deep RL) approaches in economics. However, in this paper, we focus on the state -of-the-art papers that employ DL, RL and DRL methods in economics issues. The main contribution s of this paper can be summarized as follows:  Classification of the existing DL, RL and DRL approaches in economics.  Providing extensive insights into the accuracy and applicability of DL, RL and DRL based economic models.  Discussing the core technologies and architecture of DRL in the economic technologies.  Proposing a general architecture of DRL in economic.  Presenting open issues and challenges in curren t deep reinforcement learning models in economic. The survey is organized as follows. We briefly review the common DL and DRL techniques in section s 2 and 3, respectively . Section 4 propose s the core architecture and applicability of DL and DRL approaches in economic. Finally , we followed the discussion plus presenting the real -world challenges in DRL model in economic s in section 5 and a conclusion to the work in section 6. 2. Methodology and taxonomy of Survey The survey adopts the Prisma standard to identify and review DL and DRL methods used in economics. As stated in [16], a systematic review based on the Prisma method includes four steps: 1) identification, 2) screening, 3) eligibility, 4) inclusion. In the identification st age, the documents are identified through an initial search among the mentioned databases. Through Thomson Reuters Web - of-Science (WoS) and Elsevier Scopus , 400 most relevant articles are identified . The screening step includes two stages on which, first, duplicate articles are eliminated. As a result, 200 unique articles moved to the next stage, where the relevance of the articles is examined on the basis of their title and abstract. The result of this step was 80 articles for further consideration. The ne xt step of Prisma model is eligibility, in which the full text of articles was read by the authors and 57 of them considered eligible for final review in this study. The last step of the Prisma model is the creation of the database of the study, which is u sed for qualitative and quantitative analysis. The database of the current study 3 of 45 comprises 57 articles and all the analysis in this study took place based on these articles. Figure 1 illustrates the steps of creating the database of the current study based on the Prism a method. Figure 1. Diagram of a systematic selection of the survey database The taxonomy of the survey is given in Figure 2. Where the notable methods of DL and DRL are presented. Figure 2. Taxonomy of the notable DL and DRL applied in Economics 4 of 45 Deep Learning Methods In this section , we review the most commonly used DL algorithms , which have been applied in various fields [16-20]. These deep networks comprise stacked auto -encoders (SAEs), deep belief networks (DBNs), convolutional neural networks (CNNs), recurrent neural networks (RNNs). A fundamental structure of a neural network is presented in the Figure 3 . Figure 3. Structure of a simple neural network Stacked Auto -Encoder s (SAEs) The basic building block of the stacked AE is called auto -encoder (AE) , which includes one visible inputs layer and one hidden layer [17]. It has two steps of the training process . In mathematics, they can be explained as the (Eq. 1 and 2 ): ℎ=𝑓(𝑤ℎ 𝑥 + 𝑏ℎ ) (1) 𝒴=𝑓(𝑤𝑦 𝑥 + 𝑏𝑦 ) (2) The hidden layer ℎ can be transformed to provide the output values 𝒴. Here , 𝑥 𝜖 ℝ𝑑 is the input values, and ℎ 𝜖 ℝ𝐿 denotes the hidden layer, i.e., encoder . 𝑤ℎ and 𝑤𝑦 represent the input -to- hidden and hidden -to-input weights, respectively. 𝑏ℎ and 𝑏𝑦 refer to the bias of the hidden and output terms and 𝑓(.) indicate s an activation fun ction. One can estimate the error term utilizing Euclidean distance for approximating input data 𝑥 while minimizing ‖𝑥−𝑦‖22. Figure 4 presents an architecture of AE. 5 of 45 Figure 4. A simple architecture of AE Deep Belief Networks (DBNs) The basic building block of deep belief networks is known as a restricted Boltzmann machine (RBM) which is a layer -wise training model [18]. It contains a two-layer network with visible and h idden units. One can exp ress the joint configuration energy of the units as (Eq. 3): 𝐸(𝑣,ℎ; 𝜃)=−∑𝑏𝑖𝑣𝑖𝑑 𝑖=1 − ∑𝑎𝑗ℎ𝑗𝐿 𝑗=1−∑∑𝑤𝑖𝑗𝑣𝑖ℎ𝑗L 𝑗=1d 𝑖=1 =-𝑏𝑇𝑣−𝑎𝑇ℎ-𝑣𝑇𝑤ℎ (3) Where 𝑏𝑖 and 𝑎𝑗 are the bias term of the visible and hidden units , respectively. Here, 𝑤𝑖𝑗 denotes the weight between the visible unit 𝑖 and hidden unit 𝑗. In RBM, the hidden units can capture an unbiased sample from the given data vector , as they are conditionally independent from knowing the visible states. One can improve the feature representation of a single RBM by cumulating diverse RBM one after anoth er, which construct s a DBN for detecting a deep hierarchical representation of the training data . Figure 5 presents a simple architecture of RBM. 6 of 45 Figure 5. A simple architecture of RBM with the hidden layers Convolutional Neural Networks (CNNs) CNNs are composed of a stack of periodic convolution layers and pooling layers with multiple fully connected layers . In the convolutional layer, CNNs employ a set of kernels to convolve the input data and intermediate features to yield various feature maps . In general, the pooling layer follows a convolutional layer, which is utilized to diminish the dimensions of feature maps and the network parameters. Finally, by utilizing the fully connected layers, these obtained maps can be transformed into feature vectors. We present the formu la of the vital parts of the CNNs , which are the convolution layers . Assume that 𝑋 be the input cube with the size of 𝑚×𝑛×𝑑 where 𝑚×𝑛 is regarding to the spatial level of 𝑋, and 𝑑 count the channels . The 𝑗-th filter sp ecified with the weight 𝑤𝑗 and bias 𝑏𝑗. Then, one can express the 𝑗-th output associated with the convolution layer as the (Eq. 4): 𝑦𝑗= ∑𝑓(𝑥𝑖∗ 𝑤𝑗 + 𝑏𝑗 )𝑑 𝑖=1 , 𝑗=1,2,…,𝑘 (4) Here the activation function 𝑓(.) is used to enhance the network 's nonlinearity. Currently, ReLU [19] is the most popular activation function that lead s to notably rapid convergence and robustness in terms of gradient vanishing [20]. Figure 6 presents the convolution procedure. Recurrent Neural Networks (RNNs) RNN s extended the conventional neural network with loops in connections and were developed in [21], which can identify patterns in sequential data and dynamic temporal specification by utilizing recurrent hidden states compared to the feedforward neural network . Suppose that 𝑥 is the input vecto r. The recurrent hidden state ℎ<𝑡> of the RNN can be updated by (Eq. 5 ): ℎ<𝑡> = {𝑜 𝑓1(ℎ<𝑡−1>,𝑥<𝑡>) 𝑖𝑓 𝑡=𝑜 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒, (5) where 𝑓1 denotes a nonlinear function, such as hyperbolic agent function. The update rule of the recurrent hidden state can be expressed as (Eq. 6 ): ℎ<𝑡> = 𝑓1(𝑢ℎ<𝑡−1>+ 𝑤𝑥<𝑡>+𝑏ℎ), (6) where 𝑤 and 𝑢 indicate the coefficient matrices for the input at the current state and the activation of recurrent hidden units at the prior ste p, respectively. 𝑏ℎ is the bias vector . Therefor e, the output 𝒴<𝑡> at time 𝑡 is presented as (Eq. 7) : 𝒴<𝑡>= 𝑓2(𝑝ℎ<𝑡>+ 𝑏𝑦). (7) Here , 𝑓 is the nonlinear function , and 𝑝 is the coefficient matrix for the activation of recurrent hidden units at the current step and 𝑏ℎ represent s the bias vector. Due to the vanishing gradient of traditional RNN, l ong-term memory (LSTM) [22] and gated recurrent unit [23] were introduced to handle huge sequential data. Convolution procedure is presented in [24]. Figure 7 illustrates a schematic for RNN. 7 of 45 (a) Kernel (b) Input (c) Output Figure 6. Convolution procedure Figure 7. An illustration of Recurrent Neural Network Deep Reinforcement Learning Methods In this section , we mainly focus on the most commonly used deep RL algorithms , such as value -based methods, policy gradient methods , and model -based methods. We first describe d how to formulate RL problem for the agent dealing with an environment while the goal is to maximize cumulative rewards. The two important characteristics of RL is, firstly that the agent has the capability of learning good behavior incrementally, secondly , the RL agent enjoys the trial -and-error experience with just dealing with the environment and gather information (see Figure 6). It is worth mentioning that RL methods are able to practically provide the most appropriate method in terms of computational e fficiency as compared to some traditional approaches. One can model the RL problem with an Markov Decision Process (MDP) w ith a 5-tuple (𝒮, 𝒜, T, ℛ, 𝜆) where 𝒮 (state -space ), 𝒜 (action space ), T ∈ [0, 1] (transition function ), ℛ (reward function ) and 𝛾 ∈ [0,1) (discount factor ). The RL agent try to search policy for the optimal expected return base on the value function 𝑉𝜋(𝑠) by (Eq. 8 ): 𝑉𝜋(𝑠) = 𝔼(∑𝛾𝑘∞ 𝑘=0𝑟𝑘+𝑡|𝑠𝑡=𝑠.𝜋)where 𝑉∗ = max 𝜋∈Π𝑉𝜋(𝑠) (8) Where: 𝑟𝑡 = 𝔼 𝑎 ~ 𝜋(𝑠𝑡,.)ℛ(𝑠𝑡,𝑎,𝑠𝑡+1), (9) ℙ(𝑠𝑡+1|𝑠𝑡,𝑎𝑡) = Τ(𝑠𝑡.𝑎𝑡.𝑠𝑡+1) with 𝑎𝑡 ~ 𝜋(𝑠𝑡. .) (10) 8 of 45 Analogously, the Q value function can be expressed as the (Eq. 11 ): 𝑄𝜋(𝑠.𝑎) = 𝔼(∑𝛾𝑘∞ 𝑘=0𝑟𝑘+𝑡|𝑠𝑡=𝑠.𝑎𝑡=𝑎.𝜋) where 𝑄∗ = max 𝜋∈Π𝑄𝜋(𝑠.𝑎) (11) One can see the general architecture of the DRL algorithms in Figure 8 adapted from [25]. Figure 8. Interaction between agent and environment and the g eneral structure of the deep reinforcement learning approaches Value -based Methods The value -based class of algorithms allow us to construct a value function for defining a policy. We discuss the Q -learning algorithm [26], the deep Q -network (DQN) algorithm [6] with great success when playing ATARI games. We then give a brief review of the improved DQN algorithm. Q-learning The basic value -based algorithm called Q-learning algorithm . Assume Q be the value function, then the optimal value of the Q -learning algorithm using the Bellman equation [27] can be expressed as the (Eq. 12 ): 𝑄∗(s.a)=(ℬ𝑄∗) (s.a) (12) Where the Bellman operator ( ℬ) can be described as (Eq.13 ): (ℬ𝐾)(𝑠,𝑎) =∑Τ(𝑠,𝑎,𝑠́) (ℛ(𝑠,𝑎,𝑠́) 𝑠́∈𝑆 +𝛾max 𝑎́ ∈ 𝒜Κ(𝑠́,𝑎́)) (13) Here , the unique optimal solution of the Q value function is 𝑄∗(s, a). One can check out the theoretical analysis of optimality Q function in discrete space with sufficient exploration guarante e in [26]. In practice, a parameterized value function is able to overcome the high dimensional problems (possibly continuous space). 9 of 45 Deep Q-networks (DQN) The DQN algorithm is presented by Mnih et al. [6] that can obtain good results for ATARI games in onlin e framework . In deep Q -learning, we make use of a neural net to estimate a complex, nonlinear Q-value function. Imagine the target function as (Eq. 14 ): 𝑌𝑘𝑄 = 𝑟 + 𝛾max 𝑎́ ∈ 𝒜Q(𝑠́,𝑎́; 𝜃̅𝑘) (14) While 𝜃̅𝑘 parameter, that define the values of the Q function at the 𝑘𝑡ℎ iteration, will be updated just every 𝐴 𝜖 ℕ iteration to keep the stability and diminish the risk of divergence. In order to bound the instabilities, DQN uses two heuristics, i.e., the ta rget Q -network and the replay memory [28]. Additionally, DQN take s the advantage of other heuristics like clipping the rewards for maintaining reasonable target values and for ensuring proper learning. An interesting aspect of DQN is that a variety of deep learning techniques are used to practically improve its performance such as preprocessing step of the inputs, convolutional layers and the optimization (stochastic gradient descent) [29]. We s howed the general scheme of the DQN algorithm [25] in Figure 9. Figure 9. Basic structure of the DQN algorithm Double DQN In Q -learning, the Q -value function utilizes the similar amount in order to pick out and to evaluate an action which one may cause overestimated values and upward bias in the algorithm respectively. Thus, the double estimator method can be used for each variable to efficiently remove the positive bias in the action estimation process [30]. The Double DQN is independent of any source of error , namely stochastic environment error. The target value function in the Doubl e DQN (DDQN) can be described as (Eq. 15 ): 𝑌𝑘𝐷𝐷𝑄𝑁 = 𝑟 + 𝛾𝑄(𝑠́,argmax 𝑎∈𝒜𝑄(𝑠́,𝑎; 𝜃𝑘); 𝜃̅𝑘) (15) Compared to Q -network, DDQN usually is able to improve stability and to obtain more accurate Q - value function as well. Distributional DQN The idea of approaches explained in the previous subsection s were to estimate the expected cumulative return. Another interesting method is to represent a value distribution which allows us to better detect 10 of 45 the inherent stochastic rewards and agent transitions in conjunction with the environment . One can define the random distribution return function associated with policy 𝜋 as follows (Eq. 16 ): Ζ𝜋 (s, a) = ℛ(s, a, 𝑆́) + 𝛾Ζ𝜋(𝑆́, 𝐴́) (16) With random state -action pairs ( 𝑆́, 𝐴́) and 𝐴́ ~ 𝜋(.|𝑆́). Thus, the Q value function can be expr essed as the (Eq. 17 ): 𝑄𝜋(s, a) = 𝔼[Ζ𝜋(s, a)] (17) In practice, the distributional Bellman equation, interact with deep learning, can play the role of the approximation function [31-33]. The main benefits of this approach are implementation of the risk- aware behavior [34] and improved learning provides a richer set of training signals [35]. Policy Gradient Methods This s ection discuss es about policy gradient (PG) methods that are frequently used algorithms in reinforcement learning [36] which belongs to a class of policy -based methods. The method is to find a neural network parameterized policy in order to maximize the expected cumulative reward [37]. Stochas tic Policy Gradient (SPG) The easiest approach to obtain the policy gradient estimator could be to utilize algorithm [38]. The general approach to deriv e the estimated gradient is as (Eq. 18 ): ∇𝜔𝜋𝜔(s, a) = 𝜋𝜔(s, a) ∇𝜔log(𝜋𝜔(s,a)) (18) While ∇𝜔𝑉𝜋𝜔(𝑠0)= 𝔼𝑠~𝜌𝜋𝜔,a~𝜋𝜔 [∇𝜔(log 𝜋𝜔(s,a))𝑄𝜋𝜔(𝑠,𝑎)] (19) Note that, in these methods the policy evaluation estimates Q -function and the policy improvement optimize the policy by taking a gradient step utilizing the value function approximation . The easy way of estimating the Q -function is to exchange it with a cumulative return from entire trajectories. A value -based method such as actor -critic methods can be used to estimate the return efficiently. In general, an entropy function can be used for the policy randomness and efficient exploration purpose. Additiona lly, it is common to employ an advantage value function where it does a measurement of comparison at the state to the expected return for each action. In practice, this replacement improves the numerical efficiency. Deterministic Policy Gradient (DPG) The DPG approach is the expected gradient of the action -value function. The deterministic policy gradient can be approximated without using an integral term over the action space. It can be demonstrated that the DPG algorithms can extremely perform better than SPG algorithms in high - dimensional action spaces [39]. NFQ and DQN algorithms can resolve the problematic discrete actions using the Deep Deterministic Policy Gradient (DDPG) [39] and the Neural Fitted Q Iteration with Continuous Actions (NFQC A) [40] algorithms, with the direct representation of a policy. An approach proposed by [41] to overcome the global optimization problem while updating greedy policy at each step. They defined a differentiable deterministic policy that can be moved to the gradient direction of value function for deriving the DDPG algorithm (Eq. 20) : ∇𝜔𝑉𝜋𝜔(𝑠0)= 𝔼𝑠~𝜌𝜋𝜔 [∇𝜔(𝜋𝜔)∇𝑎(𝑄𝜋𝜔(𝑠,𝑎))|a= 𝜋𝜔(𝑠)] (20) 11 of 45 Which shows that the (Eq. 20) is based on ∇𝑎(𝑄𝜋𝜔(𝑠,𝑎)). Actor -Critic Methods An actor -critic architecture is a common approach where the actor updates the policy distribution with policy gradients and the critic estimate the value function for the current policy [42] (Eq. 21) . ∇𝜔𝑉𝜋𝜔(𝑠0)= 𝔼𝑠~𝜌𝜋𝛽,𝑎~ 𝜋𝛽[∇𝜃(log 𝜋𝜔(s,a)𝑄𝜋𝜔(𝑠,𝑎)) ]. (21) where 𝛽 called behavior policy that makes the gradient biased and the critic with parameter 𝜃 estimate the value function, 𝑄(𝑠,𝑎;𝜃), with the current policy 𝜋. In deep reinforcement learning , the actor -critic functions can be parameterized with nonlinear neural networks [36]. Proposed approach by Sutton [7] was quite simple but not computationally efficient. The ideal is to design an architecture to profit from the reasonably fast reward propagation, the stability and the capability using replay memory . However, the new approach utilized in actor -critic framework presented by Wang et al. [43] and Gruslys et al. [44] have sample efficiency and computationally efficient as well . Combining policy gradient and Q-learning In order to improve the policy strategy in RL , an efficient technique needs to be engaged like policy gradient where applying a sample efficient approach and value function approximation associated with the policy . These algorithms enable us to work with continuous action spaces, to construct the policies for explicit exploration and to apply to multiagent setting where the problem deals with the stochastic optimal policy. However, the idea of combining policy gradient methods with optimal policy Q -learning was proposed by O Donoghue et al. [45] while summing the equation 2.24 with an entropy function (Eq. 22): ∇𝜔𝑉𝜋𝜔(𝑠0)= 𝔼s,a [∇𝜔(log 𝜋𝜔(s,a))𝑄𝜋𝜔(𝑠,𝑎)] + 𝛼𝔼𝑠[∇𝜔Η𝜋𝜔(s)] (22) Where Η𝜋(s) = - ∑ 𝜋(s,a) 𝑎 log𝜋(s,a) (23) It showed that in some specific settings, both valu e-based and policy -based approaches have quite similar structure [46-48]. Model -based Methods We have discussed so far, the value -based or the policy -based which belong to the method model -free approach. In this section , we focus on the model -based approach where the model deals with the dynamics of the environment and reward function. Pure model -based methods When the explicit model is unknown, it can be learned from experience by the function approximators [49-51]. The model plays the actual environment role to recommend an action. The common approach in the case of discrete actions is look ahead search , and trajectory optimization can be utilized in continuous case . A lookahead search is to generate potential trajectories with the difficulty of exploration and exploitation trade -off in sampling trajectories. The popular approaches to lookahead search are Monte Carlo tree search (MCTS) methods such that the MCTS algorithm 12 of 45 recommends an action (see Figure 9). Recently, instead of using explicit tree search techniques, learning an end-to-end model w as developed [52] with improved sample efficiency and performance as well. Lookahead search techniques is useless continuous environment. Another approach is PILCO so that apply Gaussian processes in order to learn a probabilistic model with reasonable sample efficiency [53]. However, the gaussian processes are just reliable in low-dimensional problem. One can take the benefit of the generalization capabilities of DL approaches to build the model of the environment in higher dimensions. For example, a DNN can be ut ilized in a latent state space [54]. Another approach aim s at leveraging the trajectory optimization like guided policy search [55] by taking a few sequences of actions and then learn s the policy from these sequences . The i llustration of the MCTS process presented in Figure 10 and adopted from [25] Figure 10. Illustration of the MCTS process Integrating model -free and model -based methods (IMF&MBM) The situation to choose whether using the model -free versus model -based approaches mainly depends on the model architecture such as policy and value function. An example to clearly explain the key point. Assume that an agent needs to pass the street randomly while the best choice is to take the step unless something unusual happens in front of the agent. In this situation using model -based approach may be problematic due to the randomness model , while a model -free approach to find the optimal policy is highly recommended. There is a possibility of integrating planning and learning to achieve a practical algorithm which is computationally efficient . In the absence of a model where the limited numbe r of trajectories is known, one approach is to build an algorithm to generalize well or to construct a model to generate more samples for model -free problem [56]. Other choice could be utilizing a model -based approach to accomplish primary tasks and apply model -free fine-tuning to achieve its goal successfully [57]. In the presence of a model, the tree search techniques directly [58]. The notion of neural network is able to combine these two approaches . The model proposed by Heess et al. [59] engaged backpropagation algorithm to estimate a value function. Another example is the work presented by Schema Networks [60] that use s prolific structured architecture where it leads to robust generalization. 3. Review Section 13 of 45 This section discusses an overview of various interesting utilization of both DL and deep RL approaches in economics. Deep Learning Application in Economics The recent attractive application of deep learning in variety of economics domains discussed in this section. Deep Learning in Stock Pricing In economical point of view, stock market value and its development are essential to business growth. In the current economic situation, there are many investors around the world that are interested in stock market in order to receive quick and better return compared to other se ctors. In presence of uncertainty and risk in the forecasting of stock pricing, bring the challenges to the researcher to design market model for prediction. Despite all advances to develop mathematical models for forecasting, but still not that successful [61]. The deep learning topic attract s scientists and practitioner as it is useful to make huge revenue while enhancing the prediction accuracy with DL methods . Table 1 presents the summarized researches developed, r ecently . Table 1. Application of deep learning in stock price prediction.