Stochastic Finance: An Introduction in Discrete Time

By Hans Föllmer, Alexander Schied. 2002

1,968 citations recorded by the source corpus.

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Citations in the corpus

Conditional and dynamic convex risk measures (2005, background): “Föllmer and Schied [8] and Frittelli and Rosazza Gianin [9] introduced independently the more general class of convex risk measures weakening the axioms of positive homogeneity and subadditivity by replacing them with convexity.”
Statistics and Quantitative Risk Management for Banking and Insurance (2014, background): “An excellent textbook treatment at the more mathematical level is Föllmer and Schied (2011).”
BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIME (2007, background): “…ZHOU The University of Oxford and The Chinese University of Hong Kong This paper formulates and studies a general continuous-time behavioral portfolio selection model under Kahneman and Tversky’s (cumulative) prospect theory, featuring S-shaped utility (value) functions and probability distortions.”
RISK MEASURES ON ORLICZ HEARTS (2009, background): “In Artzner et al. (1997, 1999) and the first part of Föllmer and Schied (2002a), future financial positions are modeled by elements of the set L( ) of all real-valued functions on a finite sample space , and a coherent, convex, or monetary risk measure is a mapping ρ : L( ) → R satisfying certain…”
Robust Strategies for Optimal Order Execution in the Almgren–Chriss Framework (2012, background): “The ubiquitous existence of model uncertainty was first emphasized by Knight (1921), but only few systematic approaches to this phenomenon exist to date; we refer to Cont (2006) and, for an overview over some material, to Föllmer & Schied (2011) and the references therein.”
Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions (2008, background): “interior of Hs(Q) viewed as a subset of the aﬃne hull it generates. Remark 8.1. The interested reader is referred to any good book on elementary stochastic ﬁnance for a more detailed deﬁnition (e.g., [11], page 27 or [10], page 65). Theorem8.2. Consider a scalar (K=1), nonlinear F-expectation EF(·|F”
Arbitrage and duality in nondominated discrete-time models (2013, background): “Our main financial results are, of course, extensions of the classical case where P is a singleton; see, for example, [19, 29] and the references therein.”
Risk measuring under model uncertainty (2010, background): “Föllmer and Schied [21] have studied static risk measures defined on the vector space of all bounded measurable maps.”
Robust utility maximization in a stochastic factor model (2006, background): “Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.”
Gini-Type Measures of Risk and Variability: Gini Shortfall, Capital Allocations, and Heavy-Tailed Risks (2017, unknown): “(1999); also Föllmer and Schied (2002)): (B1) Monotonicity : ρ(X) ≤ ρ(Y ) when X, Y ∈ X are such that X ≤ Y P-almost surely.”
Optimal risk sharing under distorted probabilities (2008, background): “For more results in this direction see [18].”
Distributionally Robust Markov Decision Processes (2010, background): “Indeed, such approach has also been developed in the mathemati cal finance community, usually in the static setup [19, 20].”
Utility maximization in incomplete markets (2005, unknown): “55 in [8] yields a strictly increasing sequence (τn)n∈N of integer valued, (B(Rm)⊗B(Hm)−B(R))-measurable functions and a mapping ξ :Rm ×Hm → Rm measurable with respect to the corresponding product σ-algebra, satisfying lim n→∞ ξτn(z,K̃)(z, K̃) = ξ(z, K̃) ∀ z ∈R , K̃ ∈H.”