Related papers: Risk Estimation in a Markov Cost Process: Lower an…
We consider the portfolio optimization with risk measured by conditional value-at-risk, based on the stress event of chosen asset being equal to the opposite of its value-at-risk level, under the normality assumption. Solvability conditions…
Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are…
We propose a multilevel stochastic approximation (MLSA) scheme for the computation of the value-at-risk (VaR) and expected shortfall (ES) of a financial loss, which can only be computed via simulations conditionally on the realisation of…
We demonstrate a limitation of discounted expected utility, a standard approach for representing the preference to risk when future cost is discounted. Specifically, we provide an example of the preference of a decision maker that appears…
Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…
The window mean-payoff objective strengthens the classical mean-payoff objective by computing the mean-payoff over a finite window that slides along an infinite path. Two variants have been considered: in one variant, the maximum window…
We assume a drift condition towards a small set and bound the mean square error of estimators obtained by taking averages along a single trajectory of a Markov chain Monte Carlo algorithm. We use these bounds to construct fixed-width…
In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for empirical risk minimizers. In the general setting, we prove sanity-check bounds in the spirit of \cite{KR99}…
Left truncated and right censored data are encountered frequently in insurance loss data due to deductibles and policy limits. Risk estimation is an important task in insurance as it is a necessary step for determining premiums under…
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 studies the safe reinforcement learning problem formulated as an episodic finite-horizon tabular constrained Markov decision process with an unknown transition kernel and stochastic reward and cost functions. We propose a…
Extending recent work of Corrado, we derive an algorithm that computes rigorous upper and lower bounds for rectangle scan probabilities for Markov increments. We experimentally examine the closeness of the bounds computed by the algorithm…
Value-at-Risk is one of the most popular risk management tools in the financial industry. Over the past 20 years several attempts to include VaR in the portfolio selection process have been proposed. However, using VaR as a risk measure in…
Estimating out-of-sample risk for models trained on large high-dimensional datasets is an expensive but essential part of the machine learning process, enabling practitioners to optimally tune hyperparameters. Cross-validation (CV) serves…
Risk averse decision making under uncertainty in partially observable domains is a fundamental problem in AI and essential for reliable autonomous agents. In our case, the problem is modeled using partially observable Markov decision…
This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…
The behaviour of a stochastic dynamical system may be largely influenced by those low-probability, yet extreme events. To address such occurrences, this paper proposes an infinite-horizon risk-constrained Linear Quadratic Regulator (LQR)…
The Value-at-Risk (VaR) is a widely used instrument in financial risk management. The question of estimating the VaR of loss return distributions at extreme levels is an important question in financial applications, both from operational…
Optimizing Conditional Value-at-risk (CVaR) using policy gradient (a.k.a CVaR-PG) faces significant challenges of sample inefficiency. This inefficiency stems from the fact that it focuses on tail-end performance and overlooks many sampled…
We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to different norms of the function are proven. By the estimation the well known…