In this talk we investigate continuous-time portfolio selection in the
Black-Scholes financial market under different investment rules: Roy’s
safety-first, Telser’s safety-first, Kataoka’s safety-first, mean-variance.
To ensure tractability of these portfolio selection problems, we restrict
ourselves to the class of trading strategies that are deterministic, Borel
measurable, bounded functions over the time horizon. We derive closed-form
optimal strategies for these problems, showing for instance that under
Roy’s safety-first rule, during longer time horizons, it is optimal to
invest less into the risky assets.