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The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…

Methodology · Statistics 2022-01-11 Ryan Thompson

In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random…

Probability · Mathematics 2009-09-01 Yuping Liu , Jin Ma

The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures…

Risk Management · Quantitative Finance 2017-08-25 Marcin Pitera , Thorsten Schmidt

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…

Machine Learning · Statistics 2020-08-28 Tomas Vaškevičius , Varun Kanade , Patrick Rebeschini

For a regression model, we consider the risk of the maximum likelihood estimator with respect to $\alpha$-divergence, which includes the special cases of Kullback-Leibler divergence, Hellinger distance and $\chi^2$ divergence. The…

Statistics Theory · Mathematics 2017-09-12 Yo Sheena

We consider the problems of estimation and optimization of two popular convex risk measures: utility-based shortfall risk (UBSR) and Optimized Certainty Equivalent (OCE) risk. We extend these risk measures to cover possibly unbounded random…

Computational Engineering, Finance, and Science · Computer Science 2025-06-03 Sumedh Gupte , Prashanth L. A. , Sanjay P. Bhat

In this paper, we study an optimal insurance problem for a risk-averse individual who seeks to maximize the rank-dependent expected utility (RDEU) of her terminal wealth, and insurance is priced via a general distortion-deviation premium…

Risk Management · Quantitative Finance 2022-02-08 Xiaoqing Liang , Ruodu Wang , Virginia Young

We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…

Numerical Analysis · Mathematics 2024-03-25 Erik Burman , Mihai Nechita , Lauri Oksanen

From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…

Numerical Analysis · Mathematics 2017-05-10 Simone Brugiapaglia , Ben Adcock , Richard K. Archibald

In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large…

Optimization and Control · Mathematics 2009-09-22 Denis Belomestny

This article improves the existing proven rates of regret decay in optimal policy estimation. We give a margin-free result showing that the regret decay for estimating a within-class optimal policy is second-order for empirical risk…

Statistics Theory · Mathematics 2017-04-24 Alexander Luedtke , Antoine Chambaz

We present an optimized rerandomization design procedure for a non-sequential treatment-control experiment. Randomized experiments are the gold standard for finding causal effects in nature. But sometimes random assignments result in…

Methodology · Statistics 2021-01-26 Adam Kapelner , Abba M. Krieger , Michael Sklar , David Azriel

We consider a renewal process which models a cumulative shock model that fails when the accumulation of shocks up-crosses a certain threshold. The ratio limit properties of the probabilities of non-failure after n cumulative shocks are…

Probability · Mathematics 2025-12-16 Mikael Escobar-Bach , Alexandre Popier , Malo Sahin

The insurance model when the amount of claims depends on the state of the insured person (healthy, ill, or dead) and claims are connected in a Markov chain is investigated. The signed compound Poisson approximation is applied to the…

Probability · Mathematics 2020-01-13 Gabija Liaudanskaitė , Vydas Čekanavičius

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…

Optimization and Control · Mathematics 2025-07-01 Johannes Milz , Thomas M. Surowiec

In this paper a class of combinatorial optimization problems is discussed. It is assumed that a solution can be constructed in two stages. The current first-stage costs are precisely known, while the future second-stage costs are only known…

Data Structures and Algorithms · Computer Science 2018-12-20 Marc Goerigk , Adam Kasperski , Pawel Zielinski

Return on Investment (ROI) is one of the most popular performance measurement and evaluation metrics. ROI analysis (when applied correctly) is a powerful tool in comparing solutions and making informed decisions on the acquisitions of…

Computational Engineering, Finance, and Science · Computer Science 2015-12-25 Alexei Botchkarev

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

Information Theory · Computer Science 2016-08-31 Jonathan Scarlett , Volkan Cevher

Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem…

Probability · Mathematics 2009-01-16 Florin Avram , Zbigniew Palmowski , Martijn R. Pistorius

We estimate the loss of value that companies might suffer from nature overexploitation. We find that global equities shed 26.8% in a scenario of unabated nature decline, while the worst-performing firms lose ~75% of their value. Our risk…

Risk Management · Quantitative Finance 2025-04-08 Ricardo Crisostomo