ataloss asked for clarification of my comment; "Here at NFB, I have demonstrated, to my own satisfaction at least, that personal utility theory influences financial planning and (do I dare say it?) SWR analysis." Here it is, in three parts.
Part the First: Being modest or cautious or something, I put in that qualifier about the demonstration satisfying me, even if it satisfied no one else. That way, I avoided claiming that I have answered the question completely, forever, and for everyone, with mathematical certitude, etc., etc.
Part the Second: Here is my purported proof that someone's personal utility function influences his financial planning. I started a thread on the subject at
http://nofeeboards.com/boards/viewtopic.php?t=956 This is a summary of my first post of May 31, 2003, on that thread. Suppose, for example, that you know exactly ahead of time what the real return on your investments will be for the next twenty years and that your stash is one million dollars invested at 4%. Does that tell you everything you need to know to plan your withdrawals? No, because the withdrawal plan depends also on your purposes and values.
If your intent is to maximize the sum of your withdrawals and end up broke, you let everything ride until the end of the 20 years and then make one massive withdrawal. (It will be $2,191,123.14)
If your intent is to take the same amount each year and end up broke, your annual withdrawal will be $73,581.75 for twenty years. Here the implicit utility function for a withdrawal is simply the number of dollars in it.
If your goal is to maximize the total utility of your withdrawals, and you use logarithmic utility, you will start with a withdrawal of $51,998.29 in the first year and increase your withdrawals gradually to $106,364.14 in the twentieth year and again end broke.
Q. E. D., which is mathematiker talk for "Quite Easily Done", meaning the proof is complete. (Isn't it?)
Part the Third: How does all this influence SWR analysis? We frequently agree around here that a retired person may not be willing to continue fixed real annual withdrawals in the face of market declines. If we admit that sort of psychological consideration into SWR analysis, then it seems reasonable also to include an explicit recognition of the planner's utility function and see where that leads us.