Parametric multi-attribute utility functions for optimal profit under risk constraints

Abstract

International audienceWe provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in an expected prospect maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random prospect under constraint that the risk measure is bounded above, he then behaves as a generalized expected utility maximizer in the following sense. The DM exhibits ambiguity with respect to a family of utility functions defined on a larger set of decisions than the original one; he adopts pessimism and performs first a minimization of expected utility over this family, then performs a maximization over a new decisions set. This economic behaviour is called maxmin under risk and studied by Maccheroni (Econ Theory 19:823-831, 2002). As an application, we make the link between an expected prospect maximization problem, subject to conditional value-at-risk being less than a threshold value, and a non-expected utility economic formulation involving loss aversion -type utility functions

Regime Switching Entropic Risk Measures on Crude Oil Pricing

“…Usually, the value of the risk aversion depends on the decision maker's behavior. In Seck et al, (Seck et al (2012)), it is shown that under the assumption of some particular formulation of a class of risk measures, maximizing a profit subject to these risk constraints is equivalent to maximizing a certain class of multi-attribute utility functions. These multi-attribute utility functions express loss aversion instead of risk aversion.…”

“…Two classes of entropic risk measures have been compared in Brandtner et al (2018), namely coherent or convex. These properties of risk measures are discussed largely in the literature and express some nice properties in terms of decision making strategies or solving complex portfolio optimization problems, see Cheridito et al (2005), Detlefsen and Scandolo (2005), Ben-Tal and Teboulle (2007), Ruszczynski and Shapiro (2004), Föllmer and Penner (2006), Seck et al (2012). Entropic risk measures have an exponential function representation.…”

Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio

“…It is useful for investors in practice to know relationships between the maximal utility approach and risk measures like for example value-at-risk (V aR) or conditional value-at-risk (CV aR). Seck et al in [35,3] examine connection between risk measures and parameterized families of loss aversion utility functions. For each risk measure they provide a class of associated utility functions, for which the problem of maximizing profit subject to a risk measure constraint and the max-min problem of optimization over the class of utility functions are equivalent.…”