Corpus ID: 222290683

Tight Bounds for a Class of Data-Driven Distributionally Robust Risk Measures

@article{Singh2020TightBF,
  title={Tight Bounds for a Class of Data-Driven Distributionally Robust Risk Measures},
  author={Derek Singh and Shuzhong Zhang},
  journal={arXiv: Optimization and Control},
  year={2020}
}
This paper expands the notion of robust moment problems to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. The classical Chebyshev-Cantelli (zeroth partial moment) inequalities, Scarf and Lo (first partial moment) bounds, and semideviation (second partial moment) in one dimension are investigated. The infinite dimensional primal problems are formulated and the simpler finite dimensional dual problems are derived. A principal motivating question is how… Expand
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References

SHOWING 1-10 OF 32 REFERENCES
Distributionally Robust XVA via Wasserstein Distance Part 1: Wrong Way Counterparty Credit Risk
This paper investigates calculations of robust CVA for OTC derivatives under distributional uncertainty using Wasserstein distance as the ambiguity measure. Wrong way counterparty credit risk can beExpand
Robust Arbitrage Conditions for Financial Markets
TLDR
This paper investigates arbitrage properties of financial markets under distributional uncertainty using Wasserstein distance as the ambiguity measure and coins the term statistical arbitrage. Expand
Distributionally Robust XVA via Wasserstein Distance: Wrong Way Counterparty Credit and Funding Risk
This paper investigates calculations of robust XVA, in particular, credit valuation adjustment (CVA) and funding valuation adjustment (FVA) for over-the-counter derivatives under distributionalExpand
Distributionally robust profit opportunities
TLDR
The notion of robust profit opportunities in financial markets is expanded to incorporate distributional uncertainty using Wasserstein distance as the ambiguity measure and some theory is developed and computational experiments are conducted. Expand
Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances
We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and theExpand
Data-driven risk-averse stochastic optimization with Wasserstein metric
TLDR
A data-driven risk-averse stochastic optimization approach with Wasserstein Metric is studied for the general distribution case and it is shown that the risk aversion of the proposed formulation vanishes as the size of historical data grows to infinity. Expand
Tight Bounds for Some Risk Measures, with Applications to Robust Portfolio Selection
TLDR
Tight bounds on the expected values of several risk measures that are of interest to us are developed, and the robust optimization problem in that case can be solved by means of semidefinite programming (SDP), if no more than two additional chance inequalities are to be incorporated. Expand
Semi-parametric upper bounds for option prices and expected payoffs
Abstract Upper bounds on the expected payoff of call and put options are derived. These bounds depend only on the mean and variance of the terminal stock price and not on its entire distribution, soExpand
Robust Wasserstein profile inference and applications to machine learning
TLDR
Wasserstein Profile Inference is introduced, a novel inference methodology which extends the use of methods inspired by Empirical Likelihood to the setting of optimal transport costs (of which Wasserstein distances are a particular case). Expand
A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions
  • I. Popescu
  • Mathematics, Computer Science
  • Math. Oper. Res.
  • 2005
TLDR
An optimization framework for computing optimal upper and lower bounds on functional expectations of distributions with special properties, given moment constraints is provided and generalizations of Chebyshev's inequality for symmetric and unimodal distributions are obtained. Expand
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