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We consider the Black--Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein--Uhlenbeck process, we establish the existence of…
Alpha signals for statistical arbitrage strategies are often driven by latent factors. This paper analyses how to optimally trade with latent factors that cause prices to jump and diffuse. Moreover, we account for the effect of the trader's…
Although there is a wide use of technical trading rules in stock markets, the profitability of them still remains controversial. This paper first presents and proves the upper bound of cumulative return, and then introduces many of…
Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of…
Classical portfolio optimization often requires forecasting asset returns and their corresponding variances in spite of the low signal-to-noise ratio provided in the financial markets. Modern deep reinforcement learning (DRL) offers a…
A hypothetical risk-neutral agent who trades to maximize the expected profit of the next trade will approximately exhibit long-term optimal behavior as long as this agent uses the vector $p = \nabla V (t, x)$ as effective microstructure…
Linear Temporal Logic (LTL) is widely used to specify high-level objectives for system policies, and it is highly desirable for autonomous systems to learn the optimal policy with respect to such specifications. However, learning the…
We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
We study an optimal portfolio problem designed for an agent operating in intraday electricity markets. The investor is allowed to trade in a single risky asset modelling the continuously traded power and aims to maximize the expected…
In this article, we develop a modular framework for the application of Reinforcement Learning to the problem of Optimal Trade Execution. The framework is designed with flexibility in mind, in order to ease the implementation of different…
Autonomous crypto trading systems often spend most of their design effort on finding entries, while exits are left to fixed rules that are rarely tested in a systematic way. This paper examines whether better stop-loss and take-profit…
Minimizing execution costs for large orders is a fundamental challenge in finance. Firms often depend on brokers to manage their trades due to limited internal resources for optimizing trading strategies. This paper presents a methodology…
Optimal Control (OC) is the process of determining control and state trajectories for a dynamic system, over a period of time, in order to optimize a given performance index. With the increasing of variables and complexity, OC problems can…
We introduce and study a simple model of a limit order-driven market. Traders in this model can either trade at the market price or place a limit order, i.e. an instruction to buy (sell) a certain amount of the stock if its price falls…
With the increasing integration of power plants into the frequency-regulation markets, the importance of optimal trading has grown substantially. This paper conducts an in-depth analysis of their optimal trading behavior in sequential…
We consider the problem of discounted optimal state-feedback regulation for general unknown deterministic discrete-time systems. It is well known that open-loop instability of systems, non-quadratic cost functions and complex nonlinear…
A recently new intelligent optimization algorithm called discrete state transition algorithm is considered in this study, for solving unconstrained integer optimization problems. Firstly, some key elements for discrete state transition…
We develop a dynamic trading strategy in the Linear Quadratic Regulator (LQR) framework. By including a price mean-reversion signal into the optimization program, in a trading environment where market impact is linear and stage costs are…
In this article, we develop a Bayesian approach to estimate parameters from time traces that originate from an overdamped Brownian particle in a harmonic potential, or Ornstein-Uhlenbeck process (OU). We show that least-square fitting the…