info:eu-repo/semantics/article
A control approach to robust utility maximization with logarithmic utility and time-consistent penalties
Autor
DANIEL HERNANDEZ HERNANDEZ
Institución
Resumen
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
facilitates the use of numerical algorithms, whose applicability is demonstrated in examples.
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