Related papers: Scalar multivariate risk measures with a single el…
Set-valued risk measures on $L^p_d$ with $0 \leq p \leq \infty$ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim…
We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging…
A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for $d$ assets with transaction costs or illiquidity and possible trading constraints are considered on a…
This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal…
In the paper a problem of risk measures on a discrete-time market model with transaction costs is studied. Strategy effectiveness and shortfall risk is introduced. This paper is a generalization of quantile hedging presented in [4].
We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…
Despite decades of research in risk management, most of the literature has focused on scalar risk measures (like e.g. Value-at-Risk and Expected Shortfall). While such scalar measures provide compact and tractable summaries, they provide a…
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a c\`adl\`ag nonlinear…
We examine weak anticipations in discrete-time and continuous-time financial markets consisting of one risk-free asset and multiple risky assets, defining a minimal probability measure associated with the anticipation that does not depend…
This paper contains an overview of results for dynamic multivariate risk measures. We provide the main results of four different approaches. We will prove under which assumptions results within these approaches coincide, and how properties…
Working in a continuous time setting, we extend to the general case of dynamic risk measures continuous from above the characterization of time consistency in terms of ``cocycle condition'' of the minimal penalty function. We prove also the…
The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…
In recent years, it has become apparent that an isolated microprudential approach to capital adequacy requirements of individual institutions is insufficient. It can increase the homogeneity of the financial system and ultimately the cost…
We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide…
Shortfall systemic (multivariate) risk measures $\rho$ defined through an $N$-dimensional multivariate utility function $U$ and random allocations can be represented as classical (one dimensional) shortfall risk measures associated to an…
We revisit the recently introduced concept of return risk measures (RRMs) and extend it by incorporating risk management via multiple so-called eligible assets. The resulting new class of risk measures, termed multi-asset return risk…
In this paper we provide a flexible framework allowing for a unified study of time consistency of risk measures and performance measures (also known as acceptability indices). The proposed framework not only integrates existing forms of…
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…
In the paper, the martingales and super-martingales relative to a regular set of measures are systematically studied. The notion of local regular super-martingale relative to a set of equivalent measures is introduced and the necessary and…
The assessment of risk based on historical data faces many challenges, in particular due to the limited amount of available data, lack of stationarity, and heavy tails. While estimation on a short-term horizon for less extreme percentiles…