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Mixture Of Consistent Stochastic Utilities And A Priori Randomness

Author

Listed:
  • MRAD MOHAMED

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

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.

Suggested Citation

  • Mrad Mohamed, 2021. "Mixture Of Consistent Stochastic Utilities And A Priori Randomness," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(01), pages 1-34, February.
    • Handle: RePEc:wsi:ijtafx:v:24:y:2021:i:01:n:s0219024921500023
    DOI: 10.1142/S0219024921500023
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