Related papers: Star-shaped Risk Measures
We consider a collection of derivatives that depend on the price of an underlying asset at expiration or maturity. The absence of arbitrage is equivalent to the existence of a risk-neutral probability distribution on the price; in…
This paper motivates the views that for complex systems, risk should be controlled by enforcing constraints in a modular way at different system levels, that the constraints can be expressed as assurance contracts and that acceptable risk…
The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…
In many areas of applied mathematics, engineering, and social and natural sciences, decentralization of information is a key aspect determining how to approach a problem. In this review article, we study information structures in a…
We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically…
Managing a portfolio to a risk model can tilt the portfolio toward weaknesses of the model. As a result, the optimized portfolio acquires downside exposure to uncertainty in the model itself, what we call "second order risk." We propose a…
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 various economic scenarios. Motivated by this…
We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random…
Hedge Funds are considered as one of the portfolio management sectors which shows a fastest growing for the past decade. An optimal Hedge Fund management requires an appropriate risk metrics. The classic CAPM theory and its Ratio Sharpe…
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions…
In this paper, we propose a novel axiomatic approach to evaluating the joint risk of multiple insurance risks under dependence uncertainty. Motivated by both the theory of expected utility and the Cobb-Dauglas utility function, we establish…
To achieve robustness of risk across different assets, risk parity investing rules, a particular state of risk contributions, have grown in popularity over the previous few decades. To generalize the concept of risk contribution from the…
We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex…
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of…
We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio…
We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and…
The main goal of this paper is to investigate under which conditions cash-subadditive convex dynamic risk measures are time-consistent. Proceeding as in Detlefsen and Scandolo \cite{detlef-scandolo} and inspired by their result, we give a…
In our previous paper, "A Unified Approach to Systemic Risk Measures via Acceptance Set" (\textit{Mathematical Finance, 2018}), we have introduced a general class of systemic risk measures that allow for random allocations to individual…
This paper concerns discrete-time infinite-horizon stochastic control systems with Borel state and action spaces and universally measurable policies. We study optimization problems on strategic measures induced by the policies in these…
Informally, a risk measure is said to be elicitable if there exists a suitable scoring function such that minimizing its expected value recovers the risk measure. In this paper, we analyze the elicitability properties of the class of return…