An agent solves an exponential utility maximisation problem that is robust to parameter misspecification and where the optimal strategy continuously adapts to new information. The agent invests in a risk-free asset and in risky stocks whose prices follow geometric diffusion processes. The agent does not know the drift parameters of the stock price dynamics, so she considers a set of alternative measures to make the investment problem robust to model misspecification and employs a continuous-time estimator to learn the value of the drift parameters as new information arrives during the investment horizon. For the two risky asset case, the agent’s value function is characterised as the solution to a non-linear PDE. We show that the value function has a stochastic representation and use it to analyse the optimal adaptive-robust strategy and to compare it with various benchmarks.
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