Related papers: Measuring risk with multiple eligible assets
In normal times, it is assumed that financial institutions operating in non-overlapping sectors have complementary and distinct outcomes, typically reflected in mostly uncorrelated outcomes and asset returns. Such is the reasoning behind…
Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two…
The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of…
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…
A method for calculating multi-portfolio time consistent multivariate risk measures in discrete time is presented. Market models for $d$ assets with transaction costs or illiquidity and possible trading constraints are considered on a…
In this paper, we search for optimal portfolio strategies in the presence of various risk measure that are common in financial applications. Particularly, we deal with the static optimization problem with respect to Value at Risk, Expected…
Regulatory requirements dictate that financial institutions must calculate risk capital (funds that must be retained to cover future losses) at least annually. Procedures for doing this have been well-established for many years, but recent…
We investigate the problem of finding upper and lower bounds for a Choquet risk measure of a nonlinear function of two risk factors, when the marginal distributions of the risk factors are ambiguous and represented by nonadditive measures…
The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and…
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…
Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore,…
The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be…
Monitoring means to observe a system for any changes which may occur over time, using a monitor or measuring device of some sort. In this paper we formulate a problem of monitoring dates of maximal risk of a financial position. Thus, the…
The banking systems that deal with risk management depend on underlying risk measures. Following the Basel II accord, there are two separate methods by which banks may determine their capital requirement. The Value at Risk measure plays an…
Recently, literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. A running example includes Cumulative prospect theory and Conditional variance at risk. Most of them can be can be…
We study submodularity for law-invariant functionals, with particular attention to convex risk measures. Expected losses are modular, and certainty equivalents are submodular exactly when the loss function is convex. Law-invariant coherent…
This paper develops an axiomatic framework for ranking metrics, a general class of functionals for evaluating and ordering financial or insurance positions. Unlike traditional risk-adjusted performance measures-such as the Sharpe ratio,…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
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…
This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time…