Coherent multiperiod risk adjusted values and Bellman’s principle

By Philippe Artzner, Freddy Delbaen, Jean-Marc Eber, D. Heath, Hyejin Ku. Annals of Operations Research, 2007

465 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f4f26d54968c4df93fd8193d0e4543045ac761f5

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Citations in the corpus

Convex risk measures and the dynamics of their penalty functions (2006, background): “was shown in [2] for dynamic coherent risk measures which are given in terms of the same representing class Q; see also [5].”
Conditional and dynamic convex risk measures (2005, background): “[2] show in a two period example (see the remark after Definition 5.”
Representation results for law invariant time consistent functions (2009, background): “From now on, we consider functionals which are cash invariant (in the literature this property is also sometimes referred to as translation invariance [2, 3]).”
Recent progress in random metric theory and its applications to conditional risk measures (2010, background): “y still treat the conditional convex risk measure of L∞-type. Based on this kind of conditional convex risk measure, the corresponding dynamic risk measures of L∞−type were developed in [11, 18], see [6, 7] for L∞−type of dynamic risk measures of bounded stochastic processes. Just as stated above in”
DISTRIBUTION‐INVARIANT RISK MEASURES, INFORMATION, AND DYNAMIC CONSISTENCY (2006, background): “…must consistently be updated, as new information becomes available, and intermediate cash flows must be taken into account, cf. Wang (1996, 1999), Riedel (2004), Artzner et al. (2003), Detlefsen (2003), Scandolo (2003), Cheridito, Delbaen, and Kupper (2004a,b,2005), and Föllmer and Penner (2004).”
Dynamic risk measures (2010, background): “Risk measures for processes were studied in [4, 30, 10, 11, 12, 13, 24, 25, 1].”
Dynamic exponential utility indifference valuation (2005, background): “(P7) It satisfies Ct(B;�) ≤Ct(B;�) for ∈[0, 1 ] and Ct(B;�) ≥Ct(B;�) for ∈ [1, ∞).”
Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure (2014, background): “As time consistency (or dynamic consistency) is a basic requirement for dynamic risk measures (see Rosazza Gianin (2006), Boda and Filar (2006), Artzner et al. (2007) and Jobert and Rogers (2008)), all the appropriate dynamic risk measures should necessarily possess certain functional structure so…”
Existence and Comparisons for BSDEs in general spaces (2010, background): “These operators, discussed in [19], are closely related to the theory of dynamic risk measures, as in [1, 3, 21] and others, as each concave nonlinear expectation E (·|Ft ) corresponds to a dynamic convex risk measure through the relationship ρt(Q) = −E (Q|Ft ).”
BETTER THAN DYNAMIC MEAN‐VARIANCE: TIME INCONSISTENCY AND FREE CASH FLOW STREAM (2012, background): “Although the definitions of “time consistency” introduced in Rosazza Gianin (2002a,b), Boda and Filar (2006), and Artzner et al. (2007) read differently, they all have their essence rooted in Bellman’s dynamic programming.”
Time-Inconsistency of VaR and Time-Consistent Alternatives (2007, unknown): “In the context of risk measurement time-consistency has been investigated among others, by Riedel (2004), Barrieu and El Karoui (2004), Detlefsen and Scandolo (2005), Cheridito et al. (2006), Delbaen (2006), Weber (2006), Artzner et al. (2007).”
RISK MEASURES AND CAPITAL REQUIREMENTS FOR PROCESSES (2006, background): “Artzner et al. (2004) discuss the interpretation of X as a portfolio value, proposing a different and formally simpler notion of translation invariance and capital requirement (see also Remark 4.9).”
Risk-averse dynamic programming for Markov decision processes (2010, background): “We may remark that condition (7) is a form of the translation property, discussed in various settings in [2,19,38].”