We propose a new iteration scheme, the Cauchy-Simplex, to optimize convex problems over the probability simplex ${“w\in\mathbb{R”}^n\ |\ \sum_i w_i=1\ \textrm{“and”}\ w_i\geq0}$. Specifically, we map the simplex to the positive quadrant of a unit sphere, envisage gradient descent in latent variables
In this paper, we revisit the relationship between investors’ utility functions and portfolio allocation rules. We derive portfolio allocation rules for asymmetric Laplace distributed $ALD(μ,σ,κ)$ returns and compare them with the mean-variance approach, which is based on Gaussian returns. We reveal
Asset price bubbles are situations where asset prices exceed the fundamental values defined by the present value of dividends. This paper presents a conceptually new perspective: the necessity of bubbles. We establish the Bubble Necessity Theorem in a plausible general class of economic models: with
When tackling binary optimization problems using quantum algorithms, the conventional Ising representation and Quantum Approximate Optimization Algorithm (QAOA) encounter difficulties in efficiently handling errors for large-scale problems involving multiple constraints. To address these challenges,
Trade prices of about 1000 New York Stock Exchange-listed stocks are studied at one-minute time resolution over the continuous five year period 2018–2022. For each stock, in dollar-volume-weighted transaction time, the discrepancy from a Brownian-motion martingale is measured on timescales of minute
Monetary policy pronouncements by Federal Open Market Committee (FOMC) are a major driver of financial market returns. We construct the largest tokenized and annotated dataset of FOMC speeches, meeting minutes, and press conference transcripts in order to understand how monetary policy influences fi
In a financial exchange, market impact is a measure of the price change of an asset following a transaction. This is an important element of market microstructure, which determines the behaviour of the market following a trade. In this paper, we first provide a discussion on the market impact observ
Optimized trade execution is to sell (or buy) a given amount of assets in a given time with the lowest possible trading cost. Recently, reinforcement learning (RL) has been applied to optimized trade execution to learn smarter policies from market data. However, we find that many existing RL methods
This research introduces a novel pairs trading strategy based on copulas for cointegrated pairs of cryptocurrencies. To identify the most suitable pairs, the study employs linear and non-linear cointegration tests along with a correlation coefficient measure and fits different copula families to gen
In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be leveraged for the purposes of control, forecasting or clusteri
The classical mean-variance portfolio selection problem induces time-inconsistent (precommited) strategies (see Zhou and Li (2000)). To overcome this time-inconsistency, Basak and Chabakauri (2010) introduce the game theoretical approach and look for (sub-game perfect Nash) equilibrium strategies, w
In this article, we introduce an algorithm called Backward Hedging, designed for hedging European and American options while considering transaction costs. The optimal strategy is determined by minimizing an appropriate loss function, which is based on either a risk measure or the mean squared error
By using the Hamiltonian formulation, we demonstrate that the Merton-Garman equation emerges naturally from the Black-Scholes equation after imposing invariance (symmetry) under local (gauge) transformations over changes in the stock price. This is the case because imposing gauge symmetry implies th
This paper is the first study to examine the time instability of the APT in the Japanese stock market. In particular, we measure how changes in each risk factor affect the stock risk premiums to investigate the validity of the APT over time, applying the rolling window method to Fama and MacBeth’s (
When the Orthogonal Chebyshev Sliding Technique was introduced it was applied to a portfolio of swaps and swaptions within the context of the FRTB-IMA capital calculation. The computational cost associated to the computation of the ES values - an essential component of the capital caluclation under
Systemic risk is a rapidly developing area of research. Classical financial models often do not adequately reflect the phenomena of bubbles, crises, and transitions between them during credit cycles. To study very improbable events, systemic risk methodologies utilise advanced mathematical and compu
We address an important yet challenging problem - modeling high-dimensional dependencies across multivariates such as financial indicators in heterogeneous markets. In reality, a market couples and influences others over time, and the financial variables of a market are also coupled. We make the fir
In this paper, we perform a comprehensive study of different covariance and precision matrix estimation methods in the context of minimum variance portfolio allocation. The set of models studied by us can be broadly categorized as: Gaussian Graphical Model (GGM) based methods, Shrinkage Methods, Thr
In this brief note, we prove that both forms of the Gerber statistic introduced in Gerber et al. (2022) are positive semi-definite.
The price movement prediction of stock market has been a classical yet challenging problem, with the attention of both economists and computer scientists. In recent years, graph neural network has significantly improved the prediction performance by employing deep learning on company relations. Howe