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We develop a theoretical trading conditioning model subject to price volatility and return information in terms of market psychological behavior, based on analytical transaction volume-price probability wave distributions in which we use…
A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time thermal bath dynamics, similar to random Ising systems. The interactions between agents change…
We investigate whether fractal markets hypothesis and its focus on liquidity and invest- ment horizons give reasonable predictions about dynamics of the financial markets during the turbulences such as the Global Financial Crisis of late…
A deterministic trading strategy by a representative investor on a single market asset, which generates complex and realistic returns with its first four moments similar to the empirical values of European stock indices, is used to simulate…
We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the…
Noncausal, or anticipative, heavy-tailed processes generate trajectories featuring locally explosive episodes akin to speculative bubbles in financial time series data. For $(X_t)$ a two-sided infinite $\alpha$-stable moving average (MA),…
We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary…
The cohomology theory for financial market can allow us to deform Kolmogorov space of time series data over time period with the explicit definition of eight market states in grand unified theory. The anti-de Sitter space induced from a…
Random walk models with log-normal outcomes fit local market observations remarkably well. Yet interconnected or recursive structures - layered derivatives, leveraged positions, iterative funding rounds - periodically produce power-law…
We present a novel methodology to quantify the "impact" of and "response" to market shocks. We apply shocks to a group of stocks in a part of the market, and we quantify the effects in terms of average losses on another part of the market…
The law of one price (LOP) broadly asserts that identical financial flows should command the same price. We show that, when properly formulated, LOP is the minimal condition for a well-defined mean-variance portfolio selection framework…
In this paper we employ deep learning techniques to detect financial asset bubbles by using observed call option prices. The proposed algorithm is widely applicable and model-independent. We test the accuracy of our methodology in numerical…
The Stock Market is a complex self-interacting system, characterized by an intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically about the possibility that…
Price limit trading rules are adopted in some stock markets (especially emerging markets) trying to cool off traders' short-term trading mania on individual stocks and increase market efficiency. Under such a microstructure, stocks may hit…
Standard methods and theories in finance can be ill-equipped to capture highly non-linear interactions in financial prediction problems based on large-scale datasets, with deep learning offering a way to gain insights into correlations in…
In this paper, we quantitatively investigate the properties of a statistical ensemble of stock prices. We focus attention on the relative price defined as $ X(t) = S(t)/S(0) $, where $ S(0) $ is the initial price. We selected approximately…
This paper deals with asset price bubbles modeled by strict local martingales. With any strict local martingale, one can associate a new measure, which is studied in detail in the first part of the paper. In the second part, we determine…
In this paper, we examine the fundamental performance limitations in the control of stochastic dynamical systems; more specifically, we derive generic $\mathcal{L}_p$ bounds that hold for any causal (stabilizing) controllers and any…
One of the first steps to understand and forecast economic downturns is identifying their frequency distribution, but it remains uncertain. This problem is common in phenomena displaying power-law-like distributions. Power laws play a…
The influence of the past price behaviour on the realized volatility is investigated in the present article. The results show that trending (drifting) prices lead to increased (decreased) realized volatility. This ``volatility induced by…