Related papers: Convergence of Optimal Expected Utility for a Sequ…

We study a robust utility maximization problem in the case of an incomplete market and logarithmic utility with general stochastic constraints, not necessarily convex. Our problem is equivalent to maximizing of nonlinear expected…

An NP-hard combinatorial optimization problem $\Pi$ is said to have an {\em approximation threshold} if there is some $t$ such that the optimal value of $\Pi$ can be approximated in polynomial time within a ratio of $t$, and it is NP-hard…

We address the problem of estimating the expected shortfall risk of a financial loss using a finite number of i.i.d. data. It is well known that the classical plug-in estimator suffers from poor statistical performance when faced with…

Logarithmic score and information divergence appear in information theory, statistics, statistical mechanics, and portfolio theory. We demonstrate that all these topics involve some kind of optimization that leads directly to regret…

In this paper, we analyze the local convergence rate of optimistic mirror descent methods in stochastic variational inequalities, a class of optimization problems with important applications to learning theory and machine learning. Our…

Black-box optimization is often encountered for decision-making in complex systems management, where the knowledge of system is limited. Under these circumstances, it is essential to balance the utilization of new information with…

We study stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to…

We consider stochastic optimization problems with the dual tasks of (i) effectively finding the optimizer and (ii) reliably conducting statistical inference for the optimal objective function value. We find that classical simulation…

We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we allow underly constraints described by…

The problem of demand inversion - a crucial step in the estimation of random utility discrete-choice models - is equivalent to the determination of stable outcomes in two-sided matching models. This equivalence applies to random utility…

Define the non-overlapping return time of a random process to be the number of blocks that we wait before a particular block reappears. We prove a Central Limit Theorem based on these return times. This result has applications to entropy…

There is a long history in machine learning of model ensembling, beginning with boosting and bagging and continuing to the present day. Much of this history has focused on combining models for classification and regression, but recently…

For a broad class of models widely used in practice for choice and ranking data based on Luce's choice axiom, including the Bradley--Terry--Luce and Plackett--Luce models, we show that the associated maximum likelihood estimation problems…

A model for decision making that generalizes Expected Utility Maximization is presented. This model, Expected Qualitative Utility Maximization, encompasses the Maximin criterion. It relaxes both the Independence and the Continuity…

In the large financial market, which is described by a model with countably many traded assets, we formulate the problem of the expected utility maximization. Assuming that the preferences of an economic agent are modeled with a stochastic…

This paper models the US-China trade conflict and attempts to analyze the (optimal) strategic choices. In contrast to the existing literature on the topic, we employ the expected utility theory and examine the conflict mathematically. In…

We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference…

The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. Closed, not necessarily convex, constraints are imposed on strategies. The optimal consumption and investment…

In arXiv:2103.15482 an estimate for suitable skew-symmetric 2-tensors was claimed. Soon after, this estimate has been exploited to claim powerful classification results: most notably, it has been employed to propose a proof of a Black Hole…

This article focuses on the work of O. Chanel and G. Chichilnisky (2013) on the flaws of expected utility theory while assessing the value of life. Expected utility is a fundamental tool in decision theory. However, it does not fit with the…