## 13 Citations

### Market-consistent pricing with acceptable risk

- Economics
- 2020

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 transaction costs…

### Fundamental theorem of asset pricing with acceptable risk in markets with frictions

- Economics
- 2020

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 transaction costs…

### Refinements of Kusuoka representations on L∞

- MathematicsOptimization
- 2022

We study Kusuoka representations of law invariant coherent risk measures on the space of bounded random variables, which says that any law invariant coherent risk measure is the supremum of integrals…

### Similar Risks Have Similar Prices: A Useful and Exact Quantification

- EconomicsInsurance: Mathematics and Economics
- 2022

### Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity

- MathematicsMathematics and Financial Economics
- 2022

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 and sharpen known…

### Automatic Fatou property of law-invariant risk measures

- MathematicsInsurance: Mathematics and Economics
- 2022

### Risk measures beyond frictionless markets

- Economics
- 2021

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-specified…

### A Framework for Measures of Risk under Uncertainty

- EconomicsSSRN Electronic Journal
- 2021

A risk analyst assesses potential financial losses based on multiple sources of information. Often, the assessment does not only depend on the specification of the loss random variable, but also…

### Concave/convex weighting and utility functions for risk: A new light on classical theorems

- Economics
- 2021

### Risk sharing under heterogeneous beliefs without convexity

- Economics
- 2021

. We consider the problem of ﬁnding Pareto-optimal allocations of risk among ﬁnitely many agents. The associated individual risk measures are law invariant, but with respect to agent-dependent and…

## References

SHOWING 1-10 OF 69 REFERENCES

### Law-invariant functionals beyond bounded positions

- Mathematics
- 2018

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 literature to a large class…

### Fatou property, representations, and extensions of law-invariant risk measures on general Orlicz spaces

- MathematicsFinance Stochastics
- 2018

A variety of results for quasiconvex, law-invariant functionals defined on a general Orlicz space, which extend well-known results from the setting of bounded random variables and prove a version of the extension result by Filipović and Svindland by replacing norm-lower semicontinuity with the Fatou property.

### Continuity properties of law-invariant (quasi-)convex risk functions on L∞

- Mathematics
- 2010

We study continuity properties of law-invariant (quasi-)convex functions $${f:L^\infty(\Omega, \mathcal{F}, \mathbb{P}) \to (-\infty,\infty]}$$ over a non-atomic probability space $${(\Omega,…

### Law invariant convex risk measures

- Mathematics
- 2005

As a generalization of a result by Kusuoka (2001), we provide the representation of law invariant convex risk measures. Very particular cases of law invariant coherent and convex risk measures are…

### Law Invariant Risk Measures Have the Fatou Property

- Mathematics
- 2005

S. Kusuoka [K 01, Theorem 4] gave an interesting dual characterizationof law invariant coherent risk measures, satisfying the Fatou property.The latter property was introduced by F. Delbaen [D 02].…

### CHOQUET INSURANCE PRICING: A CAVEAT

- Economics
- 2004

We show that, if prices in a market are Choquet expectations, the existence of one frictionless asset may force the whole market to be frictionless. Any risky asset will cause this collapse if prices…

### A CLASS OF DISTORTION OPERATORS FOR PRICING FINANCIAL AND INSURANCE RISKS

- Mathematics
- 2000

This article introduces a class of distortion operators, ga(t) = D[44-(u) + a], where D is the standard normal cumulative distribution. For any loss (or asset) variable X with a probability…