Adversarial Attacks on Deep Algorithmic Trading Policies

Deep Reinforcement Learning (DRL) has become an appealing solution to algorithmic trading such as high frequency trading of stocks and cyptocurrencies. However, DRL have been shown to be susceptible to adversarial attacks. It follows that algorithmic trading DRL agents may also be compromised by such adversarial techniques, leading to policy manipulation. In this paper, we develop a threat model for deep trading policies, and propose two attack techniques for manipulating the performance of such policies at test-time. Furthermore, we demonstrate the effectiveness of the proposed attacks against benchmark and real-world DQN trading agents.

Comprehensive Review of Deep Reinforcement Learning Methods and Applications in Economics

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) and deep learning (DL) for handling sophisticated dynamic business environments offers vast opportunities. 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 work, we first consider a brief review of DL, RL, and deep RL methods in diverse applications in economics providing an in-depth insight into the 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 accuracy as compared to the traditional algorithms while facing real economic problems at the presence of risk parameters and the ever-increasing uncertainties.

Pricing American Call Options by the Black-Scholes Equation with a Nonlinear Volatility Function

In this paper we investigate a nonlinear generalization of the Black-Scholes equation for pricing American style call options in which the volatility term may depend on the underlying asset price and the Gamma of the option. We propose a numerical method for pricing American style call options by means of transformation of the free boundary problem for a nonlinear Black-Scholes equation into the so-called Gamma variational inequality with the new variable depending on the Gamma of the option. We apply a modified projective successive over relaxation method in order to construct an effective numerical scheme for discretization of the Gamma variational inequality. Finally, we present several computational examples for the nonlinear Black-Scholes equation for pricing American style call option under presence of variable transaction costs.

Analytical and numerical results for American style of perpetual put options through transformation into nonlinear stationary Black-Scholes equations

We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the nonlinear Black Scholes equation with a nonlinear volatility arises from option pricing models including, e.g., non-zero transaction costs, investors preferences, feedback and illiquid markets effects and risk from unprotected portfolio. We present a method how to transform the problem of American style of perpetual put options into a solution of an ordinary differential equation and implicit equation for the free boundary position. We finally present results of numerical approximation of the early exercise boundary, option price and their dependence on model parameters.