Related papers: Portfolio Optimization under Expected Shortfall: C…
We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected loss that occurs with certain probability penalized by the dispersion of results that are worse than such an expectation. SDR combines Expected…
We propose a new class of monetary risk measures for assessing financial and ESG risk. The construction is based on classical shortfall risk measures with loss function replaced by a multi-attribute utility function. We present an extensive…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…
In risk management, often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for such failure probabilities and analyze its…
This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic…
We account for time-varying parameters in the conditional expectile-based value at risk (EVaR) model. The EVaR downside risk is more sensitive to the magnitude of portfolio losses compared to the quantile-based value at risk (QVaR). Rather…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
The effective sample size (ESS) measures the informational value of a probability distribution in terms of an equivalent number of study participants. The ESS plays a crucial role in estimating the Expected Value of Sample Information…
${\rm CoVaR}$ is one of the most important measures of financial systemic risks. It is defined as the risk of a financial portfolio conditional on another financial portfolio being at risk. In this paper we first develop a Monte-Carlo…
In recent years, the evaluation of the minimal investment risk of the quenched disordered system of a portfolio optimization problem and the investment concentration of the optimal portfolio has been actively investigated using the analysis…
Machine learning is vital in high-stakes domains, yet conventional validation methods rely on averaging metrics like mean squared error (MSE) or mean absolute error (MAE), which fail to quantify extreme errors. Worst-case prediction…
This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the…
Value at Risk (VaR) and stress testing are two of the most widely used approaches in portfolio risk management to estimate potential market value losses under adverse market moves. VaR quantifies potential loss in value over a specified…
The Stochastic Approximation EM (SAEM) algorithm, a variant stochastic approximation of EM, is a versatile tool for inference in incomplete data models. In this paper, we review the fundamental EM algorithm and then focus especially on the…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
This paper introduces \emph{biased mean regression}, estimating the \emph{biased mean}, i.e., $\mathbb{E}[Y] + x$, where $x \in \mathbb{R}$. The approach addresses a fundamental statistical problem that covers numerous applications. For…
Motivated by the Basel 3 regulations, recent studies have considered joint forecasts of Value-at-Risk and Expected Shortfall. A large family of scoring functions can be used to evaluate forecast performance in this context. However, little…
Portfolio optimization is a critical task in investment. Most existing portfolio optimization methods require information on the distribution of returns of the assets that make up the portfolio. However, such distribution information is…
Generally, in the financial literature, the notion of quadratic VaR is implicitly confused with the Delta-Gamma VaR, because more authors dealt with portfolios that contains derivatives instruments. In this paper, we postpone to estimate…