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This paper investigates performance attribution measures as a basis for constraining portfolio optimization. We employ optimizations that minimize expected tail loss and investigate both asset allocation (AA) and the selection effect (SE)…
We consider a single-period portfolio selection problem for an investor, maximizing the expected ratio of the portfolio utility and the utility of a best asset taken in hindsight. The decision rules are based on the history of stock returns…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
We develop a novel procedure for estimating the optimizer of general convex stochastic optimization problems of the form $\min_{x\in\mathcal{X}} \mathbb{E}[F(x,\xi)]$, when the given data is a finite independent sample selected according to…
This paper considers risk-sensitive model predictive control for stochastic systems with a decision-dependent distribution. This class of systems is commonly found in human-robot interaction scenarios. We derive computationally tractable…
The optimal strategies for a long-term static investor are studied. Given a portfolio of a stock and a bond, we derive the optimal allocation of the capitols to maximize the expected long-term growth rate of a utility function of the…
This paper focuses on convex constrained optimization problems, where the solution is subject to a convex inequality constraint. In particular, we aim at challenging problems for which both projection into the constrained domain and a…
Saddle point optimization is a critical problem employed in numerous real-world applications, including portfolio optimization, generative adversarial networks, and robotics. It has been extensively studied in cases where the objective…
Motivated by applications in clinical trials and finance, we study the problem of online convex optimization (with bandit feedback) where the decision maker is risk-averse. We provide two algorithms to solve this problem. The first one is a…
We study the problem of portfolio insurance from the point of view of a fund manager, who guarantees to the investor that the portfolio value at maturity will be above a fixed threshold. If, at maturity, the portfolio value is below the…
In the paper, we generalize the approach Gasnikov et. al, 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle, to the convex-concave saddle-point problem. The proposed approach works,…
In this paper, we refine and generalize closed forms for worst-case law invariant convex risk measures with uncertainty sets based on: i) closed balls under $p$-norms and Wasserstein distance; and ii) moment constraints involving mean and…
Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…
In this paper, we analyze the continuous armed bandit problems for nonconvex cost functions under certain smoothness and sublevel set assumptions. We first derive an upper bound on the expected cumulative regret of a simple bin splitting…
Applying robust optimization often requires selecting an appropriate uncertainty set both in shape and size, a choice that directly affects the trade-off between average-case and worst-case performances. In practice, this calibration is…
A highly relevant problem of modern finance is the design of Value-at-Risk (VaR) optimal portfolios. Due to contemporary financial regulations, banks and other financial institutions are tied to use the risk measure to control their credit,…
This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose…
Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex…
While Robust Model Predictive Control considers the worst-case system uncertainty, Stochastic Model Predictive Control, using chance constraints, provides less conservative solutions by allowing a certain constraint violation probability…
We study the convex-concave bilinear saddle-point problem $\min_x \max_y f(x) + y^\top Ax - g(y)$, where both, only one, or none of the functions $f$ and $g$ are strongly convex, and suitable rank conditions on the matrix $A$ hold. The…