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We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of…

We consider reinforcement learning with performance evaluated by a dynamic risk measure. We construct a projected risk-averse dynamic programming equation and study its properties. Then we propose risk-averse counterparts of the methods of…

Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law…

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…

We derive a consistent differential representation for the dynamics of a self-financing portfolio for different hedging strategies. In the basis of the derivation there is the so called "retarded action principle", which represents the…

We study continuous-time mean--variance portfolio selection in markets where stock prices are diffusion processes driven by observable factors that are also diffusion processes, yet the coefficients of these processes are unknown. Based on…

We introduce predictable relative forward performance processes (PRFPP) as a new framework for studying portfolio management within a competitive and incomplete market environment. Each agent trades a distinct stock following a binomial…

In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the percentile criterion, which minimizes the probability of a catastrophic failure. Unfortunately,…

In this paper, we search for optimal portfolio strategies in the presence of various risk measure that are common in financial applications. Particularly, we deal with the static optimization problem with respect to Value at Risk, Expected…

Managing a portfolio to a risk model can tilt the portfolio toward weaknesses of the model. As a result, the optimized portfolio acquires downside exposure to uncertainty in the model itself, what we call "second order risk." We propose a…

We develop an averaging approach to robust risk measurement under payoff uncertainty. Instead of taking a worst-case value over an uncertainty neighborhood, we weight nearby payoffs more heavily under a chosen metric and average the…

We investigate the concept of network momentum, a novel trading signal derived from momentum spillover across assets. Initially observed within the confines of pairwise economic and fundamental ties, such as the stock-bond connection of the…

Traditional portfolio management methods can incorporate specific investor preferences but rely on accurate forecasts of asset returns and covariances. Reinforcement learning (RL) methods do not rely on these explicit forecasts and are…

Considering non-stationary environments in online optimization enables decision-maker to effectively adapt to changes and improve its performance over time. In such cases, it is favorable to adopt a strategy that minimizes the negative…

In this paper, we investigate the features and the performance of the Risk Parity (RP) portfolios using the Mean Absolute Deviation (MAD) as a risk measure. The RP model is a recent strategy for asset allocation that aims at equally sharing…

Policy gradient methods, which have been extensively studied in the last decade, offer an effective and efficient framework for reinforcement learning problems. However, their performances can often be unsatisfactory, suffering from…

We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal…

A fractal approach to the long-short portfolio optimization is proposed. The algorithmic system based on the composition of market-neutral spreads into a single entity was considered. The core of the optimization scheme is a fractal walk…

This paper studies the continuous time mean-variance portfolio selection problem with one kind of non-linear wealth dynamics. To deal the expectation constraint, an auxiliary stochastic control problem is firstly solved by two new…

This paper addresses allocation methodologies for a risk measure inherited from ruin theory. Specifically, we consider a dynamic value-at-risk (VaR) measure defined as the smallest initial capital needed to ensure that the ultimate ruin…