We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades. On the one hand, we prove that when the rank of the positive semidefinite matrix in the decomposition … Read more
The purpose of this paper is to generalize the framework of activity analysis discussed in Villar (2003) and obtain similar results concerning solvability. We generalize the model due to Villar (2003), without requiring any dimensional requirements on the activity matrices and by introducing a model of activity analysis in which each activity may (or may … Read more
We study a robust monopoly pricing problem where a seller aspires to sell an item to a buyer. We assume that the seller, unaware of the buyer’s willingness to pay, ambitiously optimizes over a space of all individual rational and incentive compatible mechanisms with a regret-type objective criterion. Using robust optimization, Kocyigit et al. (2021) … Read more
We consider the portfolio optimization problem with contextual information that is available to better quantify and predict the uncertain returns of assets. Motivated by the regime modeling techniques for the finance market, we consider the setting where both the uncertain returns and the contextual information follow a Gaussian Mixture (GM) distribution. This problem is shown … Read more
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex space of random variables. It implies, in particular, the necessity of scenario-wise optimality conditions that are behind many fundamental … Read more
We present a spatial and time-continuous Ramsey-type equilibrium model for households and firms that interact on a spatial domain to model labor mobility in the presence of commuting costs. After discretization in space and time, we obtain a mixed complementarity problem that represents the spatial equilibrium model. We prove existence of equilibria using the theory … Read more
One of the biggest challenges in quantitative finance is the efficient allocation of capital. Thus, in this study, a two-step methodology was proposed, in which a combination of logistic regression and Markowitz model was performed to determine optimized portfolios. In this context, in the first step, fundamentalist indicators were used as inputs to the logistic … Read more
We propose the first weather-based algorithmic trading strategy on a continuous intraday power market. The strategy uses neither production assets nor power demand and generates profits purely based on superior information about aggregate output of weather-dependent renewable production. We use an optimized parametric policy based on state-of-the-art intraday updates of renewable production forecasts and evaluate … Read more
Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for high-dimensional optimal stopping that are popular in practice produce deterministic linear policies — policies that deterministically stop based on the … Read more
It is well known that the classical Markowitz model for portfolio optimization is extremely sensitive to estimation errors on the expected asset returns. Robust optimization mitigates this issue. We focus on ellipsoidal uncertainty sets around the point estimates of the expected asset returns. We investigate the performance of diagonal estimation-error matrices in the description of … Read more