Related papers: Spectral Risk Measures and the Choice of Risk Aver…
The relationship between set-valued risk measures for processes and vectors on the optional filtration is investigated. The equivalence of risk measures for processes and vectors and the equivalence of their penalty function formulations…
Risk measures connect probability theory or statistics to optimization, particularly to convex optimization. They are nowadays standard in applications of finance and in insurance involving risk aversion. This paper investigates a wide…
Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of…
In natural phenomena, data distributions often deviate from normality. One can think of cataclysms as a self-explanatory example: events that occur almost never, and at the same time are many standard deviations away from the common…
Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function…
In an incomplete market, including liquidly-traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise…
The rapid growth of e-commerce has made people accustomed to shopping online. Before making purchases on e-commerce websites, most consumers tend to rely on rating scores and review information to make purchase decisions. With this…
We propose a novel class of convex risk measures, based on the concept of the Fr\'echet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk…
The design and operation of protective systems is an essential engineering responsibility. Ensuring public safety, while essential, must be accomplished at a feasible cost and within government regulation. Hence, protective system design…
Distributional reinforcement learning (RL) -- in which agents learn about all the possible long-term consequences of their actions, and not just the expected value -- is of great recent interest. One of the most important affordances of a…
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…
This note will extend the research presented in Brown & Rogers (2009) to the case of CRRA agents. We consider the model outlined in that paper in which agents had diverse beliefs about the dividends produced by a risky asset. We now assume…
In this paper, we discuss various problems in the usage and definition of risk matrices. We give an overview of the general process of risk assessment with risk matrices and ordinal scales. Furthermore, we explain the fallacies in each…
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…
In recent years, the analysis of a control barrier function has received considerable attention because it is helpful for the safety-critical control required in many control application problems. While the extension of the analysis to a…
We introduce a method that allows the evaluation of general expressions for the spectral functions of the one-dimensional Hubbard model for all values of the on-site electronic repulsion U. The spectral weights are expressed in terms of…
The spectral width and sharpness of unfolded, observed GRB spectra have been presented as a new tool to infer physical properties about GRB emission via spectral fitting of empirical models. Following the tradition of the 'line-of-death',…
We characterize when a convex risk measure associated to a law-invariant acceptance set in $L^\infty$ can be extended to $L^p$, $1\leq p<\infty$, preserving finiteness and continuity. This problem is strongly connected to the statistical…
We study risk-aware linear policy approximations for the optimal operation of an energy system with stochastic wind power, storage, and limited fuel. The resulting problem is a sequential decision-making problem with rolling forecasts. In…
Credit ratings are widely used by investors as a screening device. We introduce and study several natural notions of risk consistency that promote prudent investment decisions in the framework of Choquet rating criteria. Three closely…