تقرير
A Rank-Dependent Theory for Decision under Risk and Ambiguity
| العنوان: | A Rank-Dependent Theory for Decision under Risk and Ambiguity |
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| المؤلفون: | Laeven, Roger J. A., Stadje, Mitja |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Quantitative Finance |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Mathematics - Probability, Quantitative Finance - Risk Management, 91B06, 91B16 |
| الوصف: | This paper axiomatizes, in a two-stage setup, a new theory for decision under risk and ambiguity. The axiomatized preference relation $\succeq$ on the space $\tilde{V}$ of random variables induces an ambiguity index $c$ on the space $\Delta$ of probabilities, a probability weighting function $\psi$, generating the measure $\nu_{\psi}$ by transforming an objective probability measure, and a utility function $\phi$, such that, for all $\tilde{v},\tilde{u}\in\tilde{V}$, \begin{align*} \tilde{v}\succeq\tilde{u} \Leftrightarrow \min_{Q \in \Delta} \left\{\mathbb{E}_Q\left[\int\phi\left(\tilde{v}^{\centerdot}\right)\,\mathrm{d}\nu_{\psi}\right]+c(Q)\right\} \geq \min_{Q \in \Delta} \left\{\mathbb{E}_Q\left[\int\phi\left(\tilde{u}^{\centerdot}\right)\,\mathrm{d}\nu_{\psi}\right]+c(Q)\right\}. \end{align*} Our theory extends the rank-dependent utility model of Quiggin (1982) for decision under risk to risk and ambiguity, reduces to the variational preferences model when $\psi$ is the identity, and is dual to variational preferences when $\phi$ is affine in the same way as the theory of Yaari (1987) is dual to expected utility. As a special case, we obtain a preference axiomatization of a decision theory that is a rank-dependent generalization of the popular maxmin expected utility theory. We characterize ambiguity aversion in our theory. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.05977 |
| رقم الأكسشن: | edsarx.2312.05977 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |