It's always good to learn from other fields, and there is much in statistics and actuarial science that finance people could put to good use. However, much of the progress in finance has come from ignoring good statistical and actuarial practice.
For example, you ask why not put a confidence interval around VaR. It's good statistical practice whenever you make an estimate, to also estimate the error. However, VaR is supposed to incorporate all uncertainty, including uncertainty of estimation (whether it does in practice is another question). Putting a confidence interval on it would mislead people about what it is.
A statitician says her prediction was correct if the distribution of errors is what was expected. This leads to a lot of happy statisticians with angry clients, sort of like the old surgeon's joke "the operation was successful but the patient died." Finance people have to measure success by making or losing money. You can't trade a confidence interval.
Resampling and bootstrapping have an important place in finance, but parametric techniques will always be paramount. The reason is that money adds. You cannot either ignore or overinterpret "outliers," you have to add up your total P&L.
I agree that there is more to finance than mean and standard deviation, but it's amazing how much you can explain with just these two concepts. Since money adds, the mean is essential. Since time period returns are very close to independent, and it's a big world of trading opportunities, and money adds, the higher order moments can usually be diversified away either through time or space.
My first financial job in 1981 was in capital markets for Prudential insurance. My job was to price actuarial contracts, for example, Prudential would bid for a cash payment today in return for paying the retirement benefits (for something called a "defined benefit plan" that went extinct in the last geologic age) of 1,000 40-year old workers. The actuaries would analyze the plan, project the employment events and mortality of the workers, and come up with a set of projected cash outflows. I was supposed to give them a price to bid to the plan sponsor. If we won the plan, I was supposed to select investments (in some cases, dedicated portfolios, I selected the actual investments; in most cases the plans were combined in "Separate Accounts" of similar plans, I would then set investment parameters like equity percentage and bond duration of these accounts).
I argued that I needed more than one set of most-likely cash flows from the actuaries, I needed to know how those flows changed with respect to inflation and the company stock (these were the most important determinants for individual plans) and general mortality and the economy (these were the most important systematic risks). Then I should not be setting static parameters or picking buy-and-hold investments, but dynamically hedging things.
The actuaries fundamentally didn't understand this, despite my extraordinary lucid and passionate presentations. Their profession was built on zero-beta risk. Their understanding of an insurance company was you made bets with people, collected the expected present value of the payoff at the risk-free rate, added your profit and trusted to diversification and the New York State Insurance Commission to prevent you from going broke. In some ways this was realistic in an era of regulated insurance costs. But you can see how annoying it was to someone fresh out of a quantitative finance PhD program.
On the investment side, the old-line traders who ran the portfolios wanted nothing to do with computer models or complex strategies. They wanted some money to run and a stable benchmark to beat. Their profession, in those days, said that their job was to make money by spotting superior securities and trading opportunities, and that the rest of the insurance company existed only to give them money to make more money with.
Fortunately the one actuary I saw eye-to-eye with got appointed Chief Actuary of Prudential (an honor a medievalist would understand), and I got a free hand. $3 billion of asset-liability dynamic hedging done with homebrew programs on a first-generation IBM PC in Visicalc and BASIC plus a few Fortran programs I wrote for a time-sharing mainframe. In those time-share days I got in the habit of prefacing all my file names with "AA," both for "Aaron" and to be first in a sort. The program for pricing a Savings Protector Contract was AASPC.BAS. Thirteen years later, I happened to see the output of a Pru pricing of a Stable Value Product (the successor to savings protectors). This 1990's era, Oracle/C++ professional implementation was still called AASPC.
This history inclines me to fight the introduction of actuarial concepts into finance. They are useful, but before importing them you have to understand why they aren't natives.
