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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 potentially heterogeneous reference…
This paper is concerned with the properties of the sets of strategic measures induced by admissible team policies in decentralized stochastic control and the convexity properties in dynamic team problems. To facilitate a convex analytical…
We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is…
Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhaps since conditional convex risk measures are neither random…
We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent…
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-specified eligible assets in order to pass a given capital…
Group formation is important in many economic contexts. The current literature on group formation assumes that individuals may join any existing group. In this paper, I consider the implications of social, geographic, and informational…
Expanding on techniques of concentration of measure, we develop a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form $(\rho(\lambda X))_{\lambda \ge 0}$,…
We study the aggregation of two risks when the marginal distributions are known and the dependence structure is unknown, under the additional constraint that one risk is smaller than or equal to the other. Risk aggregation problems with the…
In this work we study the Lebesgue property for convex risk measures on the space of bounded c\`adl\`ag random processes ($\mathcal{R}^\infty$). Lebesgue property has been defined for one period convex risk measures in \cite{Jo} and earlier…
We consider the risk sharing problem for capital requirements induced by capital adequacy tests and security markets. The agents involved in the sharing procedure may be heterogeneous in that they apply varying capital adequacy tests and…
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…
Regulatory and contractual constraints on individual exposures are standard in insurance and reinsurance markets, but a poorly designed constraint can distort the economic incentives of risk-averse agents. In the unconstrained problem, the…
In order to properly manage risk, practitioners must understand the aggregate risks they are exposed to. Additionally, to properly price policies and calculate bonuses the relative riskiness of individual business units must be well…
We study the problem of portfolio insurance from the point of view of a fund manager, who guarantees to the investor that the portfolio value at maturity will be above a fixed threshold. If, at maturity, the portfolio value is below the…
The dramatic increase of autonomous systems subject to variable environments has given rise to the pressing need to consider risk in both the synthesis and verification of policies for these systems. This paper aims to address a few…
We study a class of dynamically consistent risk measures that robustify a time-homogeneous Markovian reference model by allowing for distributional uncertainty in its transition laws. We start from one-step convex risk evaluations in which…
Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic…
In this research, starting from a widely accepted definition of risk, we support the idea that risk reduction is a more realistic objective than risk minimization, which represents a theoretical utopia. Furthermore, significant risk…
We study a non-concave optimization problem in which a financial company maximizes the expected utility of the surplus under a risk-based regulatory constraint. For this problem, we consider four different prevalent risk constraints…