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Decision Analysis
Published in Richard E. Neapolitan, Xia Jiang, Artificial Intelligence, 2018
Richard E. Neapolitan, Xia Jiang
We only briefly introduced notions like risk preferences and sensitivity analysis. There are many more considerations. For example, the exponential utility function is a constant risk-aversion utility function because one’s total wealth does not affect the decision obtained using the function. A decreasing risk-averse utility function can obtain a different decision depending on one’s total wealth. In sensitivity analysis we can model sensitivity to the values of the outcomes besides the probabilities. These matters and more are discussed in texts such as [Clemen, 1996] and [Neapolitan and Jiang, 2007].
Foundations of Risk and Decision Theory
Published in C. Ariel Pinto, Paul R. Garvey, Advanced Risk Analysis in Engineering Enterprise Systems, 2016
C. Ariel Pinto, Paul R. Garvey
A special type of utility function known as the exponential utility function (Kirkwood, 1997) can represent a broad class of utility function shapes or risk attitudes. Similar in form to the exponential value function, the following defines the exponential utility function.
Robust optimal asset–liability management with delay and ambiguity aversion in a jump-diffusion market
Published in International Journal of Control, 2022
To proceed, the utility function of the investor has the following form: where m and η are two positive constants representing the absolute risk aversion and weight of the average performance on the terminal wealth. In some ways, the exponential utility function is a ‘good’ utility function because it has a constant absolute risk aversion preference and is widely used in the financial literature. Furthermore, we choose a suitable form of preference parameters followed by Yuan and Mi (2021) as which are state dependent. Here, , are the ambiguity-aversion coefficients w.r.t. diffusion and jump risks. Applying the technique in Section 2, the HJB equation is given by In what follows, we are about to take four steps to derive the value function and robust optimal strategy. First of all, we conjecture the structure of the candidate value function. Then, according to the first-order optimality conditions, we obtain the candidate optimal control . Furthermore, substituting the candidate optimal control into the HJB equation, we derive the explicit solution of the HJB equation by separating the variables. At last, we verify that the solution of the HJB equation satisfies the conditions in the verification theorem. Then, the candidate value function is indeed the value function.
Risk-sensitive control of branching processes
Published in IISE Transactions, 2021
There is also criticism against the use of expected-utility criteria all together to represent preferences over alternatives with uncertain payoffs. One such criticism is based on empirical work (e.g., Schoemaker, 1980; Friedman et al., 2014) that suggests that this representation does not reflect actual human decision-making behavior. The purpose of this article is prescriptive rather than descriptive; in other words, it aims to identify “good” decisions rather than determining the decisions that are actually chosen by individuals. Using the exponential utility with varying degrees of risk sensitivity can help elicit the risk–reward tradeoffs associated with different policies and selection of policies that yield acceptable expected rewards while avoiding disastrous outcomes.
Fuzzy belief propagation in constrained Bayesian networks with application to maintenance decisions
Published in International Journal of Production Research, 2020
Ke Wang, Yan Yang, Jian Zhou, Mark Goh
In the context of the utility functions, the expected utility model proposed by Neumann and Morgenstern delineates the decision-maker's preference under uncertain outcomes (Park, Ahn, and Lee 2014). Various utility functional forms have been developed mathematically to reflect the decision-making process (Thomas 2016). Since the exponential utility function satisfies the constant absolute risk aversion property, it is often used to evaluate the utility of the decision-maker under uncertain outcomes, and is frequently adopted in various domains (Choi and Ruszczyński 2011; Park, Ahn, and Lee 2014).