In this paper, we propose new risk measures from a regulator's perspective on the regulatory capital requirements for insurers. The proposed risk measures possess many desired properties including monotonicity, translation-invariance, positive homogeneity, subadditivity, nonnegative loading, and...

We study risk sharing games with quantile-based risk measures and heterogeneous beliefs, motivated by the use of internal models in finance and insurance. Explicit forms of Pareto-optimal allocations and competitive equilibria are obtained by solving various optimization problems. For Expected...

A basic assumption of the classic reinsurance model is that the distribution of the loss is precisely known. In practice, only partial information is available for the loss distribution due to the lack of data and estimation error. We study a distributionally robust reinsurance problem by...

A basic assumption of the classic reinsurance model is that the distribution of the loss is precisely known. In practice, only partial information is available for the loss distribution due to the lack of data and estimation error. We study a distributionally robust reinsurance problem by...

In this paper, we introduce a class of optimized certainty equivalent based on the variational preference, give its dual representation based on ϕ-divergence, and study its equivalent characterization of positive homogeneity and coherence. As applications, we investigate the properties of...

In this paper, we investigate the asymptotic behavior of the portfolio diversification ratio based on Value-at-Risk (quantile) under dependence uncertainty, which we refer to as "worst-case diversification limit." We show that the worst-case diversification limit is equal to the upper limit of...

We incorporate a notion of risk aversion favoring prudent decisions from financial institutions into regulatory capital calculation principles. In the context of Basel III, IV as well as Solvency II, regulatory capital calculation is carried out through the tools of monetary risk measures. The...

Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein distributionally robust optimization (DRO), achieves this by...

This paper investigates whether and when fractional degree stochastic dominance rules can inherit the invariance properties of integer-degree stochastic dominance. Within a general formulation, we first show that it is impossible for fractional degree stochastic dominance to obey all the six...

Motivated by recent advances on elicitability of risk measures and practical considerations of risk optimization, we introduce the notions of Bayes pairs and Bayes risk measures. Bayes risk measures are the counterpart of elicitable risk measures, extensively studied in the recent literature....