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In this paper we consider Fourier transform techniques to efficiently compute the Value-at-Risk and the Conditional Value-at-Risk of an arbitrary loss random variable, characterized by having a computable generalized characteristic…
We study a class of stochastic optimal design problems for elliptic partial differential equations in divergence form, where the coefficients represent mixtures of two conducting materials. The objective is to minimize a generalized risk…
Robust Markov Decision Processes (RMDPs) have received significant research interest, offering an alternative to standard Markov Decision Processes (MDPs) that often assume fixed transition probabilities. RMDPs address this by optimizing…
This paper studies a mean-risk portfolio choice problem for log-returns in a continuous-time, complete market. This is a growth-optimal problem with risk control. The risk of log-returns is measured by weighted Value-at-Risk (WVaR), which…
Numerical challenges inherent in algorithms for computing worst Value-at-Risk in homogeneous portfolios are identified and solutions as well as words of warning concerning their implementation are provided. Furthermore, both conceptual and…
In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we…
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…
We propose nonparametric estimators for conditional value-at-risk (CVaR) and conditional expected shortfall (CES) associated with conditional distributions of a series of returns on a financial asset. The return series and the conditioning…
Though deep reinforcement learning (DRL) has obtained substantial success, it may encounter catastrophic failures due to the intrinsic uncertainty of both transition and observation. Most of the existing methods for safe reinforcement…
In this paper, we study general monetary risk measures (without any convexity or weak convexity). A monetary (respectively, positively homogeneous) risk measure can be characterized as the lower envelope of a family of convex (respectively,…
By mid 2004, the Basel Committee on Banking Supervision (BCBS) is epected to launch its final recommendations on minimum capital requirements in the banking industry. Although there is the intention to arrive at capital charges which concur…
In this paper we study variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions. We introduce stochastic approximation schemes that employ an empirical estimate of the CVaR at each iteration to…
A new realized conditional autoregressive Value-at-Risk (VaR) framework is proposed, through incorporating a measurement equation into the original quantile regression model. The framework is further extended by employing various Expected…
This article is focused on using a new measurement of risk-- Weighted Value at Risk to develop a new method of constructing initiate from the TVAR solving problem, based on MATLAB software, using the historical simulation method (avoiding…
This paper addresses risk averse constrained optimization problems where the objective and constraint functions can only be computed by a blackbox subject to unknown uncertainties. To handle mixed aleatory/epistemic uncertainties, the…
Risk management is a prominent issue in peer-to-peer lending. An investor may naturally reduce his risk exposure by diversifying instead of putting all his money on one loan. In that case, an investor may want to minimize the Value-at-Risk…
We study risk-sensitive Reinforcement Learning (RL), where we aim to maximize the Conditional Value at Risk (CVaR) with a fixed risk tolerance $\tau$. Prior theoretical work studying risk-sensitive RL focuses on the tabular Markov Decision…
We develop a variant of the stochastic prox-linear method for minimizing the Conditional Value-at-Risk (CVaR) objective. CVaR is a risk measure focused on minimizing worst-case performance, defined as the average of the top quantile of the…
This paper derives -- considering a Gaussian setting -- closed form solutions of the statistics that Adrian and Brunnermeier and Acharya et al. have suggested as measures of systemic risk to be attached to individual banks. The statistics…
The Solvency II Directive and Solvency Assessment and Management (the South African equivalent) give a Solvency Capital Requirement which is based on a 99.5% Value-at-Risk (VaR) calculation. This calculation involves aggregating individual…