# Comparing cost of two alternative given their distribution

I have distribution for cost of two alternative through Monte Carlo simulation. The distributions are not normal. Given the benefit of the two alternatives is the same but ungiven, I want to choose the alternative with less cost for a risk aversive stakeholder. (I can't simply choose the one with smaller E(c)-a*var(c) since the distribution is not normal)

• Hi Mohsen, welcome to Quant.SE! I think you have to model the risk averseness of the investor to answer this. For example, you need to have some view how volatility and skewness interact. – Bob Jansen Feb 4 '15 at 14:09
• You are right. But I need something even simpler. If I had the distribution of values for each alternative, I could easily apply a risk aversive utility function to the samples and then calculate the the expected utility. But I only have costs and I know profit is the same. – Mohsen Feb 4 '15 at 14:15
• @Mohsen There are many ways to formulate a utility function for a risk averse investor. In the general case you cant even be sure the distributions have fininte variance! You can look into the topics of first order and, probably more relevant, second order stochastic dominance. This would include a big class of utility functions. Another way would be too look at utlity functions that include a risk measure of your choice that does not explicitly use variance such as value at risk or interquartile range and rank the alternatives accordingly. – vanguard2k Feb 4 '15 at 14:46
• @vanguard2k thanks. I need a utility function that accept only cost. Most of the risk aversive utility functions I reviews are defined for positive value. – Mohsen Feb 4 '15 at 17:50
• OK, in that case: can't you argue that initial wealth should be included in the optimal choice? If you can you can just subtract the costs from that amount. – Bob Jansen Feb 4 '15 at 21:38