MIXTURE OF CONSISTENT STOCHASTIC UTILITIES AND A PRIORI RANDOMNESS

Mrad Mohamed ()
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Mrad Mohamed: LAGA, UMR CNRS 7539, Université Sorbonne Paris Nord Institut Galilée, 99 avenue J.B. Clément 93430 Villetaneuse France

International Journal of Theoretical and Applied Finance (IJTAF), 2021, vol. 24, issue 01, 1-34

Abstract: The purpose of this paper is to develop an explicit construction of consistent utilities, using the stochastic flows approach developed in El Karoui & Mrad (2013, 2020). Starting from a family of utility functions indexed by some parameter α (for example, the risk aversion coefficient or any other parameter), the idea is to randomize α and to construct nonstandard stochastic utility processes. Two approaches are developed. The first one consists of building directly from the class {Uα,α ∈ ℝ} a global utility U as a sup-convolution. The second approach which is very different, consists to define from the class (Xα,Yα) α∈ℝ of monotonic optimal processes, associated with the class {Uα,α ∈ ℝ}, a global pair (X∗,Y∗) as a mixture. The nonstandard stochastic utility is then obtained by composing stochastic flows and is 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; stochastic flows; stochastic partial differential equation; aggregated utilities; aggregated portfolios (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0219024921500023

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