Do risk lovers invest in self-protection?

- Some risk lovers choose a positive level of self-protection investment.
- Risk aversion and downside risk aversion both affect optimal self-protection.
- Comparative statics results are provided.

We show that there is a class of risk lovers who optimally choose a positive level of self-protection investment. In most cases, a risk lover increases his self-protection investment as he becomes less downside risk averse.