Related papers: Multivariate Optimized Certainty Equivalent Risk M…
In risk-sensitive learning, one aims to find a hypothesis that minimizes a risk-averse (or risk-seeking) measure of loss, instead of the standard expected loss. In this paper, we propose to study the generalization properties of…
De Finetti's optimal reinsurance is a set of contracts, one for each risk in a portfolio, that caps the retained aggregate variance to a pre-specified level while minimizing total expected loss. The premiums are determined using the…
A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the…
A classical result in risk measure theory states that every coherent risk measure has a dual representation as the supremum of certain expected value over a risk envelope. We study this topic in more detail. The related issues include: 1.…
The paper analyzes risk assessment for cash flows in continuous time using the notion of convex risk measures for processes. By combining a decomposition result for optional measures, and a dual representation of a convex risk measure for…
Estimating Monte Carlo error is critical to valid simulation results in Markov chain Monte Carlo (MCMC) and initial sequence estimators were one of the first methods introduced for this. Over the last few years, focus has been on…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…
The project managers who deal with risk management are often faced with the difficult task of determining the relative importance of the various sources of risk that affect the project. This prioritisation is crucial to direct management…
In the framework of Embedded Value new standards, namely the MCEV norms, the latest principles published in June 2008 address the issue of market and underwriting risks measurement by using stochastic models of projection and valorization.…
We propose novel scale-invariant error estimators for the Monte Carlo and multilevel Monte Carlo estimation of mean and variance. For any linear transformation of the distribution of the quantity of interest, the computation cost across…
Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures…
In this paper we present a framework for risk-averse model predictive control (MPC) of linear systems affected by multiplicative uncertainty. Our key innovation is to consider time-consistent, dynamic risk metrics as objective functions to…
We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…
Expanding on techniques of concentration of measure, we develop a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form $(\rho(\lambda X))_{\lambda \ge 0}$,…
A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a…
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…
We establish epigraphical and uniform laws of large numbers for sample-based approximations of law invariant risk functionals. These sample-based approximation schemes include Monte Carlo (MC) and certain randomized quasi-Monte Carlo…
In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk…
This paper proposes an algorithm to calculate the maximal probability of unsafety with respect to trajectories of a stochastic process and a hazard set. The unsafe probability estimation problem is cast as a primal-dual pair of…