FORTUNE — In 2002, Lord Peter Levene signed on as the first chairman of

As he prepares to leave his post this coming October, Levene sat down with Fortune to discuss where the insurance market is headed and why being an outsider can be a good thing. Unless, of course, you’re dealing with the U.S. government. Below is an edited transcript of the conversation.

FORTUNE: I understand your hiring was a break in tradition at Lloyd’s.

PL: When I joined Lloyd’s, I was the first-ever chairman in 300-something years who had come from outside the insurance industry. As it so happens, our chief executive now also came from outside the industry. That raised a few eyebrows, but he’s done a great job.

What do you think you brought to the company as an outsider?

I could question our totally accepted norms and procedures, just for the sake of questioning them. I had the ability to say “look, you’ve got all this jargon, and I haven’t the faintest idea what you’re talking about.”

For the first part of my career, I spent 20 years in the defense industry, which I did understand. Very suddenly, I was asked to change sides and be the head of defense acquisition for the UK. Well, did I understand that business? I understood it inside out and backwards. Did I understand how to run a government department? Didn’t have a clue.

It was a huge culture shock. And there’s a certain amount of — if you will excuse the word — bullshitting involved. People would come in and explain everything to me and I would go “yes yes yes.” And then I would go in and ask my staff, “what the hell was he talking about?”

After a while, you pick it up. But your question is a very good one: How can you express your authority on something if you don’t really know what you’re talking about? And the answer is you’ve got to learn very quickly.

As you near your final months at Lloyd’s, are there any specific victories that stand out in your mind?

When I started, Lloyd’s [of London] was a bit of a dirty word — it was a bad scene. Now Lloyd’s is the gold standard. We’ve moved back to where we were a long time ago, that’s the one thing that I would particularly want to claim credit for.

And trying to get Lloyd’s out of its comfort zone. When I started nine years ago, people said, “why are you going into China, what the hell’s going to happen in China?”

Nobody says that anymore.

Lloyd’s has been in the insurance business in the U.S. for 200 years. We are now reaping the benefits in this country of what the early pioneers of the Lloyd’s market did 100 years ago. What we’re doing right now in China, Brazil and Russia will in due course become very big business.

Any projects that got away from you?  

When I first started in 2002, just after 9/11, I found out that there is a rule in the U.S. that says if you are an “alien” reinsurer, you have to post collateral in cash for all the business you write. Then I found out, a domestic reinsurer, do you know how much collateral they have to post? None.

And I went to Washington and made all sorts of fuss about it and I said, ”We’re your biggest and best allies in the world, and you’re treating us like aliens?” And got nowhere. Except right now, in New York State, they have just agreed to reduce that 100% collateral to 20%. But they told me they were going to do this years ago.

It was one of the first tasks I had to deal with, this question of reinsurance collateral in the U.S., along with getting a license to operate from scratch in the Republic of China. When I started, I said give me a few months with the U.S. and it’ll be fixed. Nine years later, we’re still at it. In China, we went in and two years later, it was done.

You say your organization’s brand has made a significant comeback since the 1990s. What kinds of obstacles are still standing in the way?

We’re in the slightly unfortunate position at the moment that there are two Lloyds in the UK. One is us and the other one is Llolyds bank. Now Lloyds bank got into a lot of trouble, and they’re slowly climbing out of it. But you go around the world and people say “Yes, we know Lloyd’s very well, what’s happening with your bank?”  I say, “that’s not our bank.”

So you get things like that, which are crazy, but if you don’t deal with them they’ll stick.

So how do you differentiate yourself?

Very easy. We have an apostrophe. You see? There, the apostrophe, it’s critical.