Comparison Methods for Stochastic Models and Risks

By Mark A. McComb. Technometrics, 2003

1,147 citations recorded by the source corpus.

Subfields: Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/584318897fa357012e792a3bce5d803fc6e9ce71

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In Management Science and Operations Research

Citations in the corpus

LINEAR BIRTH/IMMIGRATION-DEATH PROCESS WITH BINOMIAL CATASTROPHES (2015, result): “This idea for a proof follows the same line of reasoning as in [58].”
Properties of hierarchical Archimedean copulas (2013, background): “This type of ordering is also called positive quadrant ordering or upper orthant ordering (see [16]).”
Consistent risk measures for portfolio vectors (2006, positive): “b) Supermodular and directionally convex ordering The supermodular ordering and the directionally convex ordering are of particular interest for multivariate risk comparison (for definition see [9] or [12, Definition 4.”
Scenario Approximations of Chance Constraints (2006, background): “It is well known that the above majorization is a partial order (e.g., [ 7 ]).”
Semi-infinite probabilistic optimization: first-order stochastic dominance constrain (2004, background): “We refer the reader to [21,22,32] for a modern perspective on stochastic ordering and to [1,13] for recent applications in statistics.”
Comparison of semimartingales and Lévy processes (2007, background): “comprehensive books survey wide areas of this research (see [15, 17, 22, 23, 24]).”
Ordering properties of the smallest and largest claim amounts in a general scale model (2017, background): “Interested readers may refer to Müller & Stoyan (2002) and Shaked & Shanthikumar (2007) for a comprehensive discussion on various stochastic orderings and relations between them.”
Generalised shot noise Cox processes (2005, background): “However, the authors’ attempt to verify this, by combining (16) to (18) and Proposition 2, failed.”
Shortest path problem considering on-time arrival probability (2009, background): “In decision theory and economics, this criterion is often called first-order stochastic dominance (see Muller and Stoyan, 2002).”
Dependence properties and bounds for ruin probabilities in multivariate compound risk models (2007, background): “We first review the notions of positive association and supermodular dependence, which can be found, for example, in Tong (1980) and in Müller and Stoyan (2002).”
Some positive dependence stochastic orders (2006, positive): “We recall (see, for example, Shaked and Shanthikumar (1994) or Müller and Stoyan (2002)) that a random vector X is said to be smaller than a random vector Y , in the upper orthant order (denoted as X ≤uo Y ), if P{X > x} ≤ P{Y > x} for all x.”
Monte Carlo sampling-based methods for stochastic optimization (2014, background): “, Müller and Stoyan [163]), which corresponds to C = R+ .”
Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles (2013, neutral): “Otherwise, f∗∗ W,V aR(x) = min{(x− d2)+, S−1 X (α)− d ∗ 2} (21)”
ORDERING PROPERTIES OF ORDER STATISTICS FROM HETEROGENEOUS POPULATIONS: A REVIEW WITH AN EMPHASIS ON SOME RECENT DEVELOPMENTS (2013, background): “For elaborate details on various stochastic orders, one may refer to Shaked and Shanthikumar [42] and Müller and Stoyan [38].”
To Split or Not to Split: Capital Allocation with Convex Risk Measures (2007, positive): “M¨uller and Stoyan, 2002) is presented.”
Dual characterization of properties of risk measures on Orlicz hearts (2008, neutral): “(6.3) Proofs of these facts and more on stochastic orders can, for instance, be found in Müller and Stoyan (2002), Föllmer and Schied (2004) or Shaked and Shanthikumar (2007).”
Stochastic Orders and Risk Measures: Consistency and Bounds (2006, positive): “M¨uller and Stoyan (2002)).”
Worst VaR scenarios (2005, background): “Then the following statements are equivalent: (a) X ≤sl Y , (b) For all real d E[X − d]+ ≤ E[Y − d]+. (20) A simple proof can be found in Müller and Stoyan (2002), Theorem 1.5.7.”