# Optimizing stochastic functions numerically

Is there an efficient and commonly used optimization method for "more complex" investment strategies. For instance, say you have a function $f(X_1,...,X_n,c,v)$ where the $X_k$'s are your random returns for each month/year $k$ which are determined by historical simulation or some model and $c,v\in[a,b]$ are parameters. (By "more complex" i mean that the function $f$ is messy enough so that optimizing it analytically is not possible.)

Hence I want to determine $\underset{c,v}{\operatorname{argmax}}g\left(f(X_1,...,X_n,c,v)\right)$ for some function $g$. Especially I'm wondering about a pension funds perspective. Then $g$ might be a risk measure such as value-at-risk or expected shortfall.

The most intuitive way would be to just simulate the random variables and determine $g(f)$ for each $c$ and $v$. However, this is very time consuming.

I saw a similar question: Portfolio optimization with monte carlo sampling from predictive distribution where stochastic optimization was suggested, but without any "concrete answer". However, my intuition tells me that this must be a fairly common problem in larger financial institutions, so there must exist optimization methods that are more often used than others.

• This sort of difficult portfolio optimization is handled quite well by the PortfolioAnalytics package. The authors wrote an informal tutorial which explains the what and how. – pteetor Nov 22 '13 at 0:02
• Thank you for your comment. It looks interesting. I wanted to try it out, but I could get it to install properly, gotta give it another try later. – Good Guy Mike Nov 22 '13 at 18:07
• Why do you need g? Can you specify some properties of f? Is f continous, differentiable, a polynomial, pathwise linear or such? – user1157 Jan 27 '14 at 22:20