Resource title

A control approach to robust utility maximization with logarithmic utility and time-consistent penalties

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Resource description

We propose a stochastic control approach to the dynamic maximization of robust utility functionals that are defined in terms of logarithmic utility and a dynamically consistent convex risk measure. The underlying market is modeled by a diffusion process whose coefficients are driven by an external stochastic factor process. In particular, the market model is incomplete. Our main results give conditions on the minimal penalty function of the robust utility functional under which the value function of our problem can be identified with the unique classical solution of a quasilinear PDE within a class of functions satisfying certain growth conditions. The fact that we obtain classical solutions rather than viscosity solutions is important for the use of numerical algorithms, whose applicability is demonstrated in examples.

Resource author

Daniel Hernández-Hernández, Alexander Schied

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Resource publish date

Resource language

eng

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text/html

Resource resource URL

http://hdl.handle.net/10419/25144

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Adapt according to the presented license agreement and reference the original author.