# Quasi-Logconvex Measures of Risk

@inproceedings{Laeven2022QuasiLogconvexMO, title={Quasi-Logconvex Measures of Risk}, author={Roger J. A. Laeven and Emanuela Rosazza Gianin}, year={2022} }

This paper introduces and fully characterizes the novel class of quasi-logconvex measures of risk, to stand on equal footing with the rich class of quasi-convex measures of risk. Quasi-logconvex risk measures naturally generalize logconvex return risk measures, just like quasi-convex risk measures generalize convex monetary risk measures. We establish their dual representation and analyze their taxonomy in a few (sub)classiﬁcation results. Furthermore, we characterize quasi-logconvex risk…

## References

SHOWING 1-10 OF 32 REFERENCES

### Portfolio Optimization with Quasiconvex Risk Measures

- MathematicsMath. Oper. Res.
- 2015

This paper describes optimal solutions of the portfolio problem associated to quasiconvex risk measures and describes the shape of the efficient frontier in the mean-risk space and some particular cases are investigated.

### Convex measures of risk and trading constraints

- MathematicsFinance Stochastics
- 2002

The notion of a convex measure of risk is introduced, an extension of the concept of a coherent risk measure defined in Artzner et al. (1999), and a corresponding extensions of the representation theorem in terms of probability measures on the underlying space of scenarios are proved.

### RISK MEASURES: RATIONALITY AND DIVERSIFICATION

- Mathematics
- 2008

When there is uncertainty about interest rates (typically due to either illiquidity or defaultability of zero coupon bonds) the cash‐additivity assumption on risk measures becomes problematic. When…

### Risk Preferences and their Robust Representation

- EconomicsMath. Oper. Res.
- 2013

This work describes the subjective notion of risk by means of a risk order and focuses on the context invariant features of diversification and monotonicity, which allows for a differentiated interpretation depending on the underlying context that is illustrated in different settings.

### OPTIMAL RISK SHARING FOR LAW INVARIANT MONETARY UTILITY FUNCTIONS

- Economics
- 2007

We consider the problem of optimal risk sharing of some given total risk between two economic agents characterized by law‐invariant monetary utility functions or equivalently, law‐invariant risk…

### CASH SUBADDITIVE RISK MEASURES AND INTEREST RATE AMBIGUITY

- Economics
- 2007

A new class of risk measures called cash subadditive risk measures is introduced to assess the risk of future financial, nonfinancial, and insurance positions. The debated cash additive axiom is…

### Coherent Measures of Risk

- Economics
- 1999

In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable…

### Entropy Coherent and Entropy Convex Measures of Risk

- Computer ScienceMath. Oper. Res.
- 2013

The properties of entropy coherent and entropy convex measures of risk are studied, their dual conjugate function is derived, and they are characterized in terms of properties of the corresponding acceptance sets.

### The Marginal Cost of Risk, Risk Measures, and Capital Allocation

- EconomicsManag. Sci.
- 2016

This work reverse the sequence of this approach by calculating the marginal costs of risk exposures for a profit maximizing financial institution with risk averse counterparties, and then identifying a closed-form solution for the risk measure whose gradient delivers the correct marginal costs.