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Despite the fact that the Euler allocation principle has been adopted by many financial institutions for their internal capital allocation process, a comprehensive description of Euler allocation seems still to be missing. We try to fill…

Optimizing risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) of a general loss distribution is usually difficult, because 1) the loss function might lack structural properties such as convexity or…

Many modern products exhibit high reliability, often resulting in long times to failure. Consequently, conducting experiments under normal operating conditions may require an impractically long duration to obtain sufficient failure data for…

We extend the Annually Recalculated Virtual Annuity (ARVA) spending rule for retirement savings decumulation to include a cap and a floor on withdrawals. With a minimum withdrawal constraint, the ARVA strategy runs the risk of depleting the…

This paper investigates risk measures derived from the expected maximum deficit in a continuous-time framework and develops optimal reserve allocation strategies across multiple lines of business. We formalize the expected maximum deficit…

Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with…

Solving chance-constrained optimal control problems for systems subject to non-stationary uncertainties is a significant challenge.Conventional robust model predictive control (MPC) often yields excessive conservatism by relying on static…

Safe Reinforcement Learning from Human Feedback (RLHF) typically enforces safety through expected cost constraints, but the expectation captures only a single statistic of the cost distribution and fails to account for distributional…

This paper presents a model-free reinforcement learning (RL) algorithm to solve the risk-averse optimal control (RAOC) problem for discrete-time nonlinear systems. While successful RL algorithms have been presented to learn optimal control…

We study risk-sensitive reinforcement learning in finite discounted MDPs, where a generative model of the MDP is assumed to be available. We consider a family or risk measures called the optimized certainty equivalent (OCE), which includes…

Maximum likelihood estimation in nonlinear models can exhibit substantial instability in finite samples when the data provide limited information about certain parameters. Such instability is driven by rare but extreme realizations of the…

This work presents a methodology to incorporate reliability constraints in the optimal power systems expansion planning problem. Besides LOLP and EPNS, traditionally used in power systems, this work proposes the use of the risk measures VaR…

The problem of finding the optimal portfolio for investors is called the portfolio optimization problem. Such problem mainly concerns the expectation and variability of return (i.e., mean and variance). Although the variance would be the…

Expected Shortfall (ES, also known as CVaR) is the most important coherent risk measure in finance, insurance, risk management, and engineering. Recently, Wang and Zitikis (2021) put forward four economic axioms for portfolio risk…

This paper addresses allocation methodologies for a risk measure inherited from ruin theory. Specifically, we consider a dynamic value-at-risk (VaR) measure defined as the smallest initial capital needed to ensure that the ultimate ruin…

Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…

We consider the problem of estimating the Optimized Certainty Equivalent (OCE) risk from independent and identically distributed (i.i.d.) samples. For the classic sample average approximation (SAA) of OCE, we derive mean-squared error as…

We consider a financial intermediary managing assets and liabilities exposed to several risk sources and seeking an optimal portfolio strategy to minimise the initial capital invested and the total risk associated with investment losses and…

Most autonomous driving safety benchmarks use time-to-collision (TTC) to assess risk and guide safe behaviour. However, TTC-based methods treat risk as a one-dimensional closing problem, despite the inherently two-dimensional nature of…

The valuation of over-the-counter derivatives is subject to a series of valuation adjustments known as xVA, which pose additional risks for financial institutions. Associated risk measures, such as the value-at-risk of an underlying…