I am familiar with the notion of two-stage stochastic optimization but I have not found any constructive examples so far, so I am stuck now on how to actually implement this on a given problem. The problem is:
Consider an investor with an initial wealth $W_0$. At time $0$, the investor constructs a portfolio comprising one riskless asset with return $R_1$ in the first period and one risky asset with return $R_1^+$ with probability $0.5$ and $R_1^−$ with probability $0.5$. At the end of the first period, the investor can rebalance her portfolio. The return in the second period is R2 for the riskless asset, while it is $R_2^+$ with probability $0.5$ and $R_2^−$ with probability $0.5$ for the risky asset. The objective is to meet a liability $L_2 = 0.9$ at the end of Period 2 and to maximize the expected remaining wealth $W_2$. Formulate a two-stage stochastic linear optimization to solves the investor’s problem.
I would deeply appreciate any helps on this!