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The stochastic volatility model is a popular tool for modeling the volatility of assets. The model is a nonlinear and non-Gaussian state space model, and consequently is difficult to fit. Many approaches, both classical and Bayesian, have…
Probabilistic time series forecasting is crucial for quantifying future uncertainty, with significant applications in fields such as energy and finance. However, existing methods often rely on computationally expensive sampling or…
We develop a dual-control method for approximating investment strategies in incomplete environments that emerge from the presence of trading constraints. Convex duality enables the approximate technology to generate lower and upper bounds…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
This paper builds a model of high-frequency equity returns by separately modeling the dynamics of trade-time returns and trade arrivals. Our main contributions are threefold. First, we characterize the distributional behavior of…
This paper deals with the extreme value analysis for the triangular arrays, which appear when some parameters of the mixture model vary as the number of observations grow. When the mixing parameter is small, it is natural to associate one…
The principle of absence of arbitrage opportunities allows obtaining the distribution of stock price fluctuations by maximizing its information entropy. This leads to a physical description of the underlying dynamics as a random walk…
We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications typically there is insufficient history to compute a sample covariance matrix (SCM) for a large number of alphas. To…
Obtaining reliable estimates of conditional covariance matrices is an important task of heteroskedastic multivariate time series. In portfolio optimization and financial risk management, it is crucial to provide measures of uncertainty and…
This paper proposes a novel stock selection strategy framework based on combined machine learning algorithms. Two types of weighting methods for three representative machine learning algorithms are developed to predict the returns of the…
Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…
Finite mixtures of regression models provide a flexible modeling framework for many phenomena. Using moment-based estimation of the regression parameters, we develop unbiased estimators with a minimum of assumptions on the mixture…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
Constrained clustering has gained significant attention in the field of machine learning as it can leverage prior information on a growing amount of only partially labeled data. Following recent advances in deep generative models, we…
Finding Bertram's optimal trading strategy for a pair of cointegrated assets following the Ornstein--Uhlenbeck price difference process can be formulated as an unconstrained convex optimization problem for maximization of expected profit…
It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard…
Regarding the intraday sequence of high frequency returns of the S&P index as daily realizations of a given stochastic process, we first demonstrate that the scaling properties of the aggregated return distribution can be employed to define…
Changes in market conditions present challenges for investors as they cause performance to deviate from the ranges predicted by long-term averages of means and covariances. The aim of conditional asset allocation strategies is to overcome…