Related papers: Monetary Risk Measures
In this work we study the Lebesgue property for convex risk measures on the space of bounded c\`adl\`ag random processes ($\mathcal{R}^\infty$). Lebesgue property has been defined for one period convex risk measures in \cite{Jo} and earlier…
We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of $\mathcal{P}$-quasisure bounded random variables, where $\mathcal{P}$ is a (possibly non-dominated) class of probability…
We study risk measures $\varphi:E\longrightarrow\mathbb{R}\cup\{\infty\}$, where $E$ is a vector space of random variables which a priori has no lattice structure$\unicode{x2014}$a blind spot of the existing risk measures literature. In…
The aim of this study is to present proofs for new theorems. Basic thoughts of new definitions emerge from the decision-making under uncertainty in economics and finance. Shape of the certain utility curve is central to standard definitions…
We propose a kernel-based nonparametric framework for mean-variance optimization that enables inference on economically motivated shape constraints in finance, including positivity, monotonicity, and convexity. Many central hypotheses in…
This paper concerns sequential computation of risk measures for financial data and asks how, given a risk measurement procedure, we can tell whether the answers it produces are `correct'. We draw the distinction between `external' and…
Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not…
The NA condition is one of the pillars supporting the classical theory of financial mathematics. We revisit this condition for financial market models where a dynamic risk-measure defined on $L^0$ is fixed to characterize the family of…
This paper is mainly a survey of recent research developments regarding methods for risk minimization in financial markets modeled by It\^o-L\'evy processes, but it also contains some new results on the underlying stochastic maximum…
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic…
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…
One of the crucial problems in mathematical finance is to mitigate the risk of a financial position by setting up hedging positions of eligible financial securities. This leads to focusing on set-valued maps associating to any financial…
Regulatory and contractual constraints on individual exposures are standard in insurance and reinsurance markets, but a poorly designed constraint can distort the economic incentives of risk-averse agents. In the unconstrained problem, the…
Under the continuous assumption on the generator $g$, Briand et al. [Electron. Comm. Probab. 5 (2000) 101--117] showed some connections between $g$ and the conditional $g$-expectation $({\mathcal{E}}_g[\cdot|{\mathcal{F}}_t])_{t\in[0,T]}$…
In this paper, we investigate the Lambda Value-at-Risk ($\Lambda$VaR) under ambiguity, where the ambiguity is represented by a family of probability measures. We establish that for increasing Lambda functions, the robust (i.e., worst-case)…
To provide a solid analytic foundation for the module approach to conditional risk measures, this paper establishes a complete random convex analysis over random locally convex modules by simultaneously considering the two kinds of…
We study the problem of portfolio insurance from the point of view of a fund manager, who guarantees to the investor that the portfolio value at maturity will be above a fixed threshold. If, at maturity, the portfolio value is below the…
Starting from the global financial crisis to the more recent disruptions brought about by geopolitical tensions and public health crises, the volatility of risk in financial markets has increased significantly. This underscores the…
The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with…
Motivated by optimal investment problems in mathematical finance, we consider a variational problem of Neyman-Pearson type for law-invariant robust utility functionals and convex risk measures. Explicit solutions are found for…