Mixture of consistent stochastic utilities, and a priori randomness

Mrad Mohamed
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Mrad Mohamed: LAGA - Laboratoire Analyse, Géométrie et Applications - UP8 - Université Paris 8 Vincennes-Saint-Denis - UP13 - Université Paris 13 - Institut Galilée - CNRS - Centre National de la Recherche Scientifique

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Abstract: The purpose of this paper is to develop an explicit construction of consistent utilities, using the stochastic flows approach developed in [KM13] and [KM16]. Starting from a family of utility functions indexed by some parameter α (for example the risk aversion of different agents), the idea is to randomize α and construct a non standard stochastic utilities processes. Two approach are developed, the first one consists to built directly from the class {U α , α ∈ R} a global one U as a sup-convolution. The second approach which is very different, consists to define from a class (X α , Y α) α∈R of monotonic processes a global pair (X * , Y *) as a mixture. The non standard stochastic utility is then obtained by composing stochastic flows and interpreted as the aggregate utility of all considered agents .

Keywords: forward utility; performance criteria; horizon-unbiased utility; consistent utility; progressive utility; portfolio optimization; optimal portfolio; duality; minimal martingale measure; Stochastic flows; Stochas- tic partial differential equation. (search for similar items in EconPapers)
Date: 2020-12-24
Note: View the original document on HAL open archive server: https://hal.science/hal-01728554v2
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Published in International Journal of Theoretical and Applied Finance, 2020

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01728554

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