Convex measures of risk and trading constraints

By Hans Föllmer, Alexander Schied. Finance and Stochastics, 2002

1,641 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/a2e0eb89cb6348c947d1035b9fb93676f18708da

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Citations in the corpus

Optimal Capital Allocation Principles (2005, positive): “Risk measures and premium principles of this general type have been proposed and investigated in Heilmann (1989), Tsanakas (2007) and Furman and Zitikis (2008a).”
Risk minimizing portfolios and HJBI equations for stochastic differential games (2008, neutral): “(See also [2], [4], [6] and [9].”
Dynamic Monetary Risk Measures for Bounded Discrete-Time Processes (2004, background): “In this section we extend the concepts of monetary, convex and coherent risk measures to our setup and prove corresponding representation results.”
Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths (2008, background): “It was proved that a sublinear expectation has the following representation (see [1, 8, 14 ]): There exists a family of linear expectations {Eθ }θ ∈� such that”
ON A CONVEX MEASURE OF DRAWDOWN RISK (2014, positive): “In the context of risk measures, convexity ensures that diversification of a portfolio does not increase risk, as formalized by Föllmer and Schied (2002, 2010, 2011).”
Portfolio diversification and value at risk under thick-tailedness (2009, neutral): “It was documented in numerous studies that the time series encountered in many fields in economics and finance are heavy-tailed (see the discussion in Loretan and Phillips 1994, Gabaix et al. 2003 and Rachev et al. 2005 and references therein). Mandelbrot (1963) presented evidence that historical da”
Risk Measures and Robust Optimization Problems (2006, background): “is the Fenchel–Legendre transform of the convex increasing loss function (x) := −u(−x); see Ref.[33], Theorem 10, Ref.”
Tail Risk of Multivariate Regular Variation (2011, background): “The general theory of coherent risk measures was developed for arbitrary real random variables in [12], and the convex measures that combine subadditivity and positive homogeneity into the convexity property were extended to càdlàg processes in [9], and to abstract spaces in [14] that include determ”
Conditional and dynamic convex risk measures (2005, background): “in terms of a so called penalty function α : P → [0,+∞]; see [6] or [9] for a proof.”
A THEORETICAL FRAMEWORK FOR THE PRICING OF CONTINGENT CLAIMS IN THE PRESENCE OF MODEL UNCERTAINTY (2006, background): “For applications of capacities that arise from a set of probabilities, we refer the reader to the theory of risk measures; see, for example, [1, 7, 14].”
Niveloids and their extensions: Risk measures on small domains (2014, methodology): “For example, in the case of Gilboa and Schmeidler [22]’s multiple priors preferences, (S,Σ) is a measurable space and an action a generating utility ua (s) in each state s is evaluated by φ (ua) = inf p∈Γ ∫ S ua (s) dp (s) (1) ∗We thank an associate editor and two anonymous referees for very useful ”
Risk-averse dynamic programming for Markov decision processes (2010, background): “Particularly relevant for us are the duality theory [1, 10, 14, 16, 17, 34, 43, 45, 46], and the theory of conditional and dynamic risk measures [2, 8, 11, 15, 18, 19, 28, 38, 48, 40, 45, 47].”
Risk minimization in financial markets modeled by Itô-Lévy processes (2014, methodology): “10} Example 1.3 (Convex risk measures) (Föllmer & Schied (2002), Frittelli & RosazzaGianin (2002)) Definition 1.4 Let p ∈ [2,∞].”