49 citations · 57 across the 17 of their papers we have counts for
25 papers
Risk, utility and sensitivity to large losses
Martin Herdegen, Nazem Khan, Cosimo Munari
Risk and utility functionals are fundamental building blocks in economics and finance. In this paper we investigate under which conditions a risk or utility functional is sensitive…
An elementary proof of the dual representation of Expected Shortfall
Martin Herdegen, Cosimo Munari
We provide an elementary proof of the dual representation of Expected Shortfall on the space of integrable random variables over a general probability space. Unlike the results in…
Robust portfolio selection under Recovery Average Value at Risk
Cosimo Munari, Justin Plückebaum, Stefan Weber
We study mean-risk optimal portfolio problems where risk is measured by Recovery Average Value at Risk, a prominent example in the class of recovery risk measures. We establish exi…
Risk measures beyond frictionless markets
Maria Arduca, Cosimo Munari
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-…
Capital Requirements and Claims Recovery: A New Perspective on Solvency Regulation
Cosimo Munari, Lutz Wilhelmy, Stefan Weber
Protection of creditors is a key objective of financial regulation. Where the protection needs are high, i.e., in banking and insurance, regulatory solvency requirements are an ins…
Law-invariant functionals that collapse to the mean: Beyond convexity
Felix-Benedikt Liebrich, Cosimo Munari
We establish general "collapse to the mean" principles that provide conditions under which a law-invariant functional reduces to an expectation. In the convex setting, we retrieve…
Fundamental theorem of asset pricing with acceptable risk in markets with frictions
Maria Arduca, Cosimo Munari
We study the range of prices at which a rational agent should contemplate transacting a financial contract outside a given securities market. Trading is subject to nonproportional…
Multi-utility representations of incomplete preferences induced by set-valued risk measures
Cosimo Munari
We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have…
Law-invariant functionals that collapse to the mean
Fabio Bellini, Pablo Koch-Medina, Cosimo Munari +1
We discuss when law-invariant convex functionals "collapse to the mean". More precisely, we show that, in a large class of spaces of random variables and under mild semicontinuity…
Adjusted Expected Shortfall
Matteo Burzoni, Cosimo Munari, Ruodu Wang
We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with diffe…
Stability properties of Haezendonck-Goovaerts premium principles
Niushan Gao, Cosimo Munari, Foivos Xanthos
We investigate a variety of stability properties of Haezendonck-Goovaerts premium principles on their natural domain, namely Orlicz spaces. We show that such principles always sati…
Dual representations for systemic risk measures based on acceptance sets
Maria Arduca, Pablo Koch-Medina, Cosimo Munari
We establish dual representations for systemic risk measures based on acceptance sets in a general setting. We deal with systemic risk measures of both "first allocate, then aggreg…
Law-invariant functionals on general spaces of random variables
Fabio Bellini, Pablo Koch-Medina, Cosimo Munari +1
We establish general versions of a variety of results for quasiconvex, lower-semicontinuous, and law-invariant functionals. Our results extend well-known results from the literatur…
A continuous selection for optimal portfolios under convex risk measures does not always exist
Michel Baes, Cosimo Munari
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…
Surplus-invariant risk measures
Niushan Gao, Cosimo Munari
This paper presents a systematic study of the notion of surplus invariance, which plays a natural and important role in the theory of risk measures and capital requirements. So far…
A simple characterization of tightness for convex solid sets of positive random variables
Pablo Koch-Medina, Cosimo Munari, Mario Šikić
We show that for a convex solid set of positive random variables to be tight, or equivalently bounded in probability, it is necessary and sufficient that it is radially bounded, i.…
Existence, uniqueness and stability of optimal portfolios of eligible assets
Michel Baes, Pablo Koch-Medina, Cosimo Munari
In a capital adequacy framework, risk measures are used to determine the minimal amount of capital that a financial institution has to raise and invest in a portfolio of pre-specif…
Fatou Property, representations, and extensions of law-invariant risk measures on general Orlicz spaces
Niushan Gao, Denny H. Leung, Cosimo Munari +1
We provide a variety of results for (quasi)convex, law-invariant functionals defined on a general Orlicz space, which extend well-known results in the setting of bounded random var…
Which eligible assets are compatible with comonotonic capital requirements?
Pablo Koch-Medina, Cosimo Munari, Gregor Svindland
Within the context of capital adequacy, we study comonotonicity of risk measures in terms of the primitives of the theory: acceptance sets and eligible, or reference, assets. We sh…
Diversification, protection of liability holders and regulatory arbitrage
Pablo Koch-Medina, Cosimo Munari, Mario Sikic
Any solvency regime for financial institutions should be aligned with the fundamental objectives of regulation: protecting liability holders and securing the stability of the finan…
Capital adequacy tests and limited liability of financial institutions
Pablo Koch-Medina, Santiago Moreno-Bromberg, Cosimo Munari
The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. The objective of this paper is to investigate, in the con…
Law-invariant risk measures: extension properties and qualitative robustness
Pablo Koch-Medina, Cosimo Munari
We characterize when a convex risk measure associated to a law-invariant acceptance set in can be extended to , , preserving finiteness and continui…
Measuring risk with multiple eligible assets
Walter Farkas, Pablo Koch-Medina, Cosimo Munari
The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability…
Beyond cash-additive risk measures: when changing the numéraire fails
Walter Farkas, Pablo Koch-Medina, Cosimo Munari
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 c…