Implications of constant risk aversion

Bamberg, Günter; Spremann, Klaus

doi:10.1007/bf01917173

Cited by 38 publications

(9 citation statements)

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“…Among all concave increasing utilities, the only one for which C u (·) is shift‐additive, is the first one, see Bamberg and Spremann (1981). Hence, we conclude that is a convex risk measure only for the class of exponential utilities Consequently, the only utility for which − C u ( X ) is a coherent risk measure (i.e., u is positively homogeneous and shift additive) is the linear utility u ( t ) = t ( b →∞ in ), in which case …”

Section: Coherent/convex Risk Measures and Other Related Certaintymentioning

confidence: 99%

An Old‐new Concept of Convex Risk Measures: The Optimized Certainty Equivalent

Ben‐Tal

Teboulle

2007

Mathematical Finance

319

246

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The optimized certainty equivalent (OCE) is a decision theoretic criterion based on a utility function, that was first introduced by the authors in 1986. This paper reexamines this fundamental concept, studies and extends its main properties, and puts it in perspective to recent concepts of risk measures. We show that the negative of the OCE naturally provides a wide family of risk measures that fits the axiomatic formalism of convex risk measures. Duality theory is used to reveal the link between the OCE and the ϕ-divergence functional (a generalization of relative entropy), and allows for deriving various variational formulas for risk measures. Within this interpretation of the OCE, we prove that several risk measures recently analyzed and proposed in the literature (e.g., conditional value of risk, bounded shortfall risk) can be derived as special cases of the OCE by using particular utility functions. We further study the relations between the OCE and other certainty equivalents, providing general conditions under which these can be viewed as coherent/convex risk measures. Throughout the paper several examples illustrate the flexibility and adequacy of the OCE for building risk measures.

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Section: Coherent/convex Risk Measures and Other Related Certaintymentioning

confidence: 99%

An Old‐new Concept of Convex Risk Measures: The Optimized Certainty Equivalent

Ben‐Tal

Teboulle

2007

Mathematical Finance

319

246

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“…The constant a captures the decision makers' extent of risk aversion (Freund, 1956). Bamberg and Spremann (1981) show how a can be determined. For risk-averse decision makers, the constant a takes positive values (Pratt, 1964).…”

Section: Value-based Business Process Managementmentioning

confidence: 99%

Capability development with process maturity models – Decision framework and economic analysis

Forstner

Kamprath

Röglinger

2014

Journal of Decision Systems

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Despite the need for sustaining competitive advantage, scholars and practitioners struggle when deciding which organizational capabilities they should develop to what extent. Today, inconsistent recommendations bear the risk of misallocating corporate funds. Despite recent advances, further research needs to be conducted with respect to how uncertainty can be considered in capability development decisions and whether the cutting of capabilities is a feasible option. Against this background, we propose a conceptual framework for structuring capability development decisions. Due to the close relationship between capability development and business process management, the framework builds on process maturity models and the principles of value-based business process management. We also conduct an economic analysis to disclose general relationships that govern capability development based on process maturity models.

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“…7 Bamberg and Spremann (1981), Epstein and Zin (1991), Friend and Blume (1975), Pindyck (1988), Pratt (1964, Safra and Segal (1998), Szpiro (1986), Tobin (1958), and Wolf and Pohlman (1983) have tested for a constant value of risk aversion.…”

Section: The Positive Feedback Modelmentioning

confidence: 99%