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In this paper, we explore the portfolio allocation problem involving an uncertain covariance matrix. We calculate the expected value of the Constant Absolute Risk Aversion (CARA) utility function, marginalized over a distribution of…
Risk aversion plays a significant and central role in investors' decisions in the process of developing a portfolio. In this framework of portfolio optimization we determine the portfolio that possesses the minimal risk by using a new…
This thesis investigates Merton's portfolio problem under two different rough Heston models, which have a non-Markovian structure. The motivation behind this choice of problem is due to the recent discovery and success of rough volatility…
Markowitz's optimal portfolio relies on the accurate estimation of correlations between asset returns, a difficult problem when the number of observations is not much larger than the number of assets. Using powerful results from random…
Portfolio management via reinforcement learning is at the forefront of fintech research, which explores how to optimally reallocate a fund into different financial assets over the long term by trial-and-error. Existing methods are…
Classical portfolio optimization methods typically determine an optimal capital allocation through the implicit, yet critical, assumption of statistical time-invariance. Such models are inadequate for real-world markets as they employ…
In the context of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios which are determined by certain transformations of linear functions of a…
We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function,…
The portfolio optimization problem is a critical issue in asset management and has long been studied. Markowitz's mean-variance model has fundamental limitations, such as the assumption of a normal distribution for returns and sensitivity…
We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise…
This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is…
The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We define two…
In this work, we deal with the problem of computing a comprehensive front of efficient solutions in multi-objective portfolio optimization problems in presence of sparsity constraints. We start the discussion pointing out some weaknesses of…
We consider the problem of selecting a portfolio of assets that provides the investor a suitable balance of expected return and risk. With respect to the seminal mean-variance model of Markowitz, we consider additional constraints on the…
The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…
This paper proposes a machine learning-based framework for asset selection and portfolio construction, termed the Best-Path Algorithm Sparse Graphical Model (BPASGM). The method extends the Best-Path Algorithm (BPA) by mapping linear and…
Covariance matrices estimated from short, noisy, and non-Gaussian financial time series are notoriously unstable. Empirical evidence suggests that such covariance structures often exhibit power-law scaling, reflecting complex, hierarchical…
Tracking a financial index boils down to replicating its trajectory of returns for a well-defined time span by investing in a weighted subset of the securities included in the benchmark. Picking the optimal combination of assets becomes a…
In the present work, the optimal portfolio minimizing the investment risk with cost is discussed analytically, where this objective function is constructed in terms of two negative aspects of investment, the risk and cost. We note the…
A new approach in stochastic optimization via the use of stochastic gradient Langevin dynamics (SGLD) algorithms, which is a variant of stochastic gradient decent (SGD) methods, allows us to efficiently approximate global minimizers of…