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Abstract

We consider an incomplete market with an untradable stochastic factor and a robust investment problem based on the CARA utility. We formulate it as a stochastic differential game problem, and use Hamilton–Jacobi–Bellman–Isaacs equations to derive an explicit representation of the robust optimal portfolio; the HJBI equation is transformed using a substitution of the Cole–Hopf type. Not only the pure investment problem, but also a problem of robust hedging is taken into account: an agent tries to hedge the risk associated with derivatives based on the stochastic factor.