Consistent Utility of Investment and Consumption: a forward/backward SPDE viewpoint

Nicole El Karoui (), Caroline Hillairet () and Mohamed Mrad ()
Additional contact information
Nicole El Karoui: LPMA; UMR CNRS 6632; Université Pierre et Marie Curie
Caroline Hillairet: LAGA; UMR CNRS 7539; Université Paris 13

No 2017-74, Working Papers from Center for Research in Economics and Statistics

Abstract: This paper provides an extension of the notion of consistent progressive utilities U to consistent progressive utilities of investment and consumption (U,V). It discusses the notion of market consistency in this forward framework, compared to the classic backward setting with a given terminal utility, and whose value function is an example of such consistent forward utility. To ensure the consistency with the market model or a given set of test processes, we establish a stochastic partial differential equation (SPDE) of Hamilton-Jacobi-Bellman (HJB)-type that U has to satisfy. This SPDE highlights the link between the utility of wealth U and the utility of consumption V, and between the drift and the volatility characteristics of the utility U. By associating with the HJB-SPDE two SDEs, we discuss the existence and the uniqueness of a concave solution. Finally, we provide explicit regularity conditions and characterize the consistent pairs of consistent utilities of investment and consumption. Some examples, such as power utilities, illustrate the theory. ;Classification-JEL: 60H15, 91B16, 91B70, 91G10

Keywords: Market-consistent progressive utility of investment and consumption; Forward/backward stochastic partial differential equation (SPDE) (search for similar items in EconPapers)
Pages: 30 pages
Date: 2017-01-26
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (3)

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