Related papers: Group cohesion under individual regulatory constra…
The standard theory of coherent risk measures fails to consider individual institutions as part of a system which might itself experience instability and spread new sources of risk to the market participants. In compliance with an approach…
Risk is unavoidable in business and risk management is needed amongst others to set up good security policies. Once the risks are evaluated, the next step is to decide how they should be treated. This involves managers making decisions on…
This paper introduces marginal fairness, a new individual fairness notion for equitable decision-making in the presence of protected attributes such as gender, race, and religion. This criterion ensures that decisions based on generalized…
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…
We study risk sharing among agents with preferences modeled by heterogeneous distortion risk measures, who are not necessarily risk averse. Pareto optimality for agents using risk measures is often studied through the lens of…
We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito, Delbaen, and Kupper (2006). These risk measures take into account not only the amounts but also the…
It is in general challenging to provide confidence intervals for individual variables in high-dimensional regression without making strict or unverifiable assumptions on the design matrix. We show here that a "group-bound" confidence…
We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…
We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on…
A deterministic trading strategy by a representative investor on a single market asset, which generates complex and realistic returns with its first four moments similar to the empirical values of European stock indices, is used to simulate…
In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by F\"ollmer, Schied (2002). The…
A collectivised fund is a proposed form of pension investment, in which all investors agree that any funds associated with deceased members should be split among survivors. For this to be a viable financial product, it is necessary to know…
This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
This paper considers an insurer with two collaborating business lines that faces three critical decisions: (1) dividend payout, (2) reinsurance coverage, and (3) capital injection between the lines, in the presence of model uncertainty. The…
We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…
Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based…
Risk aggregation is a popular method used to estimate the sum of a collection of financial assets or events, where each asset or event is modelled as a random variable. Applications, in the financial services industry, include insurance,…
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…
We consider the problem of minimizing capital at risk in the Black-Scholes setting. The portfolio problem is studied given the possibility that a correlation constraint between the portfolio and a financial index is imposed. The optimal…