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Consumption optimization for recursive utility in a jump-diffusion model

Fabio Antonelli () and Carlo Mancini ()
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Fabio Antonelli: University of L’Aquila
Carlo Mancini: University of L’Aquila

Decisions in Economics and Finance, 2016, vol. 39, issue 2, 293-310

Abstract: 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.

Keywords: BSDEs; Jump-diffusion processes; Recursive utility; Consumption process; Homogeneity; Inverse problem (search for similar items in EconPapers)
JEL-codes: C02 G11 G14 (search for similar items in EconPapers)
Date: 2016
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