An investor has an initial wealth WQ that must be allocated between a risk-free asset, with certain return r{, and a risky asset. We assume a simple binomial model of uncertainty, like we did in Section 3.1. The return of the risky asset will either be ρ u or R¿, with probabilities pu and p¿, respectively.

• Find the optimal allocation of wealth if the investor has an exponential utility function, like Eq. (13.11), with absolute risk aversion a.
• How does the value of the initial wealth influence the result?