Dynamic quasi concave performance measures |
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| Institution: | 1. Department of Economics and Management, University of Pisa, Italy;2. CNRS, CMAP - Ecole Polytechnique, France;1. GAINS, Université du Mans, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France;2. CREM, Université de Caen, Campus 1, Esplanade de la Paix, 14032 Caen Cedex 5, France;1. Department of Mathematics, University of Pavia, Via A. Ferrata 1, 27100 Pavia, Italy;2. Faculdade de Ciencias da Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal;1. Social Sciences Division, Yale-NUS College, 6 College Avenue East #07-19, Singapore 138614, Singapore;2. Department of Economics, Brown University, Providence, RI 02912, USA;1. School of Finance, Renmin University of China, China;2. Department of Economics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong |
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| Abstract: | We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and certainty equivalent to conditional acceptability indexes. We provide the characterization of a CPM in terms of an induced family of conditional convex risk measures. In the case of indexes these risk measures are coherent. Then, Dynamic Performance Measures (DPMs) are introduced and the problem of time consistency is addressed. The definition of time consistency chosen here ensures that the positions which are considered good tomorrow are already considered good today. Finally, we investigate the relation between time consistency for a DPM and weak acceptance consistency for the induced families of risk measures. |
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| Keywords: | Conditional performance measure Conditional acceptability index Induced family of risk measures Dynamic performance measure Time consistency Risk to reward ratio |
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