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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 survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target…

Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…

In this paper, we document a novel machine learning based bottom-up approach for static and dynamic portfolio optimization on, potentially, a large number of assets. The methodology applies to general constrained optimization problems and…

Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial…

This paper considers mean-variance optimization under uncertainty, specifically when one desires a sparsified set of optimal portfolio weights. From the standpoint of a Bayesian investor, our approach produces a small portfolio from many…

Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances…

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…

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…

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…

In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton-Jacobi-Bellman equation…

In this paper, we consider the optimal portfolio liquidation problem under the dynamic mean-variance criterion and derive time-consistent solutions in three important models. We give adapted optimal strategies under a reconsidered…

This survey reviews portfolio choice in settings where investment opportunities are stochastic due to, e.g., stochastic volatility or return predictability. It is explained how to heuristically compute candidate optimal portfolios using…

We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk…

One of the reasons that higher order moment portfolio optimization methods are not fully used by practitioners in investment decisions is the complexity that these higher moments create by making the optimization problem nonconvex. Many few…

We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to managing the Value at Risk (VaR) assuming a heavy tailed distribution of…

This survey is an introduction to asymptotic methods for portfolio-choice problems with small transaction costs. We outline how to derive the corresponding dynamic programming equations and simplify them in the small-cost limit. This allows…

We study a utility maximization problem in a financial market with a stochastic drift process, combining a worst-case approach with filtering techniques. Drift processes are difficult to estimate from asset prices, and at the same time…

This work initiates research into the problem of determining an optimal investment strategy for investors with different attitudes towards the trade-offs of risk and profit. The probability distribution of the return values of the stocks…

This paper proposes a new method for financial portfolio optimization based on reducing simultaneous asset shocks across a collection of assets. This may be understood as an alternative approach to risk reduction in a portfolio based on a…