Consumption in incomplete markets

Paolo Guasoni () and Gu Wang ()
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Paolo Guasoni: Dublin City University
Gu Wang: Worcester Polytechnic Institute

Finance and Stochastics, 2020, vol. 24, issue 2, No 5, 383-422

Abstract: Abstract We develop a method to find approximate solutions, and their accuracy, to consumption–investment problems with isoelastic preferences and infinite horizon, in incomplete markets where state variables follow a multivariate diffusion. We construct upper and lower contractions; these are fictitious complete markets in which state variables are fully hedgeable, but their dynamics is distorted. Such contractions yield pointwise upper and lower bounds for both the value function and the optimal consumption of the original incomplete market, and their optimal policies are explicit in typical models. Approximate consumption–investment policies coincide with the optimal one if the market is complete or utility is logarithmic.

Keywords: Portfolios; Consumption; Incomplete markets; Power utility; 91G10; 91G80 (search for similar items in EconPapers)
JEL-codes: G11 G12 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00780-020-00420-9

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