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送料無料 日付更新(2017年7月)

1,000円以上の注文で3%OFFクーポン(0823-29)

目次

  • 1 Introduction
  • 2 Mathematical Preliminaries
    • 2.1 Interpretation of the mathematical concepts
    • 2.2 Some notation and definitions from integration theory
    • 2.3 Some results on atomless spaces
    • 2.4 Commonotonicity
    • 2.5 Quantiles and Rearrangements
    • 2.6 Some basic theorems from functional analysis
    • 2.7 The Fenchel−Legendre transform
    • 2.8 The transform of a concave function
  • 3 Value at Risk
    • 3.1 Definition and properties of Quantiles
    • 3.2 Definition of VaR
    • 3.3 Shortcomings
  • 4 Coherent and Concave Utility Functions
    • 4.1 Monetary Utility Functions
    • 4.2 Characterisation of coherent risk measures
    • 4.3 The Fatou Property
    • 4.4 Some Examples
    • 4.5 Characterisation of coherent utility functions with the Fatou property
    • 4.6 The relation between S and Sba
    • 4.7 Weak compactness of S
    • 4.8 Concave utility functions,duality results
    • 4.9 Extension of a Fatou utility function
    • 4.10 Gâteaux differentiability of utility functions,subgradient
    • 4.11 A class of examples
    • 4.12 Concave utility functions,reduction technique,weak compactness
    • 4.13 The one‐sided derivative
    • 4.14 Relevance:Halmos−Savage theorem
    • 4.15 Ordering on utility functions,monotone convergence
    • 4.16 Utility functions defined on bigger spaces
  • 5 Law Determined Monetary Utility Functions
    • 5.1 The Fatou property
    • 5.2 A Representation of probability measures as nonincreasing functions
    • 5.3 Law Determined Utilities
    • 5.4 Weak compactness property
  • 6 Operations on utility functions
    • 6.1 Minimum of two coherent utility functions
    • 6.2 Minimum of concave utility functions
    • 6.3 Inf Convolution of coherent utility functions
    • 6.4 The inf convolution of concave utility functions
    • 6.5 Product of coherent utiity functions
  • 7 Convex games and utility functions
    • 7.1 Non‐emptiness of the core
    • 7.2 Commonotone utility functions
    • 7.3 Distortion
    • 7.4 Strongly exposed points
  • 8 Relation with VaR
    • 8.1 VaR and TailVaR
    • 8.2 VaR as an envelope of coherent utilities
  • 9 The Capital Allocation Problem
    • 9.1 Simple game theoretic approach
    • 9.2 A stronger concept of fairness
  • 10 The extension of risk measures to L0
    • 10.1 L0 and utility functions
    • 10.2 Coherent functions defined on L0
  • 11 Dynamic utility functions in a two period model
    • 11.1 Notation for the two period case
    • 11.2 Time Consistency
  • 12 Finite and discrete Time
    • 12.1 Time Consistency
    • 12.2 Supermartingale property,potentials,submartingales
    • 12.3 Refinement for the case Q《P