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Consumption optimization for recursive utility in a jump-diffusion model

Author

Listed:
  • Fabio Antonelli

    (University of L’Aquila)

  • Carlo Mancini

    (University of L’Aquila)

Abstract

In this paper, we consider a market model with prices and consumption following a jump-diffusion dynamics. In this setting, we first characterize the optimal consumption plan for an investor with recursive stochastic differential utility on the basis of his/her own beliefs, then we solve the inverse problem to find what beliefs make a given consumption plan optimal. The problem is viewed in general for a class of homogeneous recursive utility, and later we choose a logarithmic model for the utility aggregator as an explicitly computable example. When beliefs, represented via Girsanov’s theorem, get incorporated into the model, the change of measure gives rise, up to a transformation, to a backward stochastic differential equation whose generator exhibits a quadratic behavior in the Brownian component and a locally Lipschitz one in the jump component, which is solvable on the basis of some recent results.

Suggested Citation

  • Fabio Antonelli & Carlo Mancini, 2016. "Consumption optimization for recursive utility in a jump-diffusion model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 293-310, November.
    • Handle: RePEc:spr:decfin:v:39:y:2016:i:2:d:10.1007_s10203-016-0177-1
    DOI: 10.1007/s10203-016-0177-1
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    References listed on IDEAS

    as
    1. Antonelli, Fabio & Mancini, Carlo, 2016. "Solutions of BSDE’s with jumps and quadratic/locally Lipschitz generator," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3124-3144.
    2. Mark Schroder & Costis Skiadas, 2008. "Optimality And State Pricing In Constrained Financial Markets With Recursive Utility Under Continuous And Discontinuous Information," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 199-238, April.
    3. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    4. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    5. Schroder, Mark & Skiadas, Costis, 2003. "Optimal lifetime consumption-portfolio strategies under trading constraints and generalized recursive preferences," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 155-202, December.
    6. Ali Lazrak & Fernando Zapatero, 2004. "Efficient Consumption Set Under Recursive Utility and Unknown Beliefs," Post-Print hal-00485712, HAL.
    7. Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, vol. 89(1), pages 68-126, November.
    8. Lazrak, Ali & Zapatero, Fernando, 2004. "Efficient consumption set under recursive utility and unknown beliefs," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 207-226, February.
    9. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    BSDEs; Jump-diffusion processes; Recursive utility; Consumption process; Homogeneity; Inverse problem;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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