From the Readers

A Job Well Done

Dear Editor:

In the February 1999 Actuarial Review, Robert Finger reviewed two books on the topic of risk. In commenting on the book, Seeing Tomorrow: Rewriting the Rules of Risk, by Dembo and Freeman, Mr. Finger states: Second, the value of the negative outcomes is based on "Regret," which

I would liken to a nonmathematical type of utility.

Not having read the book in question, I cannot comment on the use of the term "regret" by Dembo and Freeman. However, in statistical decision theory, the term "regret" does have a specific mathematical meaning. The following discussion of the regret function relies heavily on Statistical Theory (Third Edition), by Bernard W. Lindgren (Macmillan, 1976).

For a given state of nature, q Î Q , and action, a Î A, there is an associated loss function, L(q ,a), assumed to be known, where Q and A represent the set of possible states of nature and the set of all possible actions respectively. The regret function is defined as:

r(q ,a) = L(q ,a) –	min L(q ,a)
	aÎA

To illustrate the regret function, consider the following example: there are two states of nature rain (q ₁) and no rain (q ₂). There are three possible actions, stay at home (a₁), go out with no umbrella (a₂), and go out with an umbrella (a₃). The loss function is given and is defined by the following table of values for L(q ,a):

	States of Nature
	rain (q 1)	no rain (q 2)
Actions
stay home	4	4
go, no umbrella	5	0
go with umbrella	2	5

Suppose it rains. Then the minimum loss is 2, no matter what action is taken. If I stay home, my loss is 4. But, since the best I could have done was to experience a loss of 2, my regret is 4-2=2. If I go out without an umbrella, my regret is 5-2=3. In the example shown above, the regret and the loss functions are the same when the state of nature is "no rain," since the minimum loss if 0. The complete regret function is shown in the following table of values for r(q ,a):

	States of Nature
	rain (q 1)	no rain (q 2)
Actions
stay home (a1)	2	4
go, no umbrella (a2)	3	0
go with umbrella (a3)	0	5

Regret can also be thought of as avoidable loss or opportunity loss.

I’m sure that someone better versed in the application of risk theory and statistical decision theory to the insurance business can illustrate the actuarial applications of the regret function. I just hope that the above has served as a modest introduction to the regret function.

Dave Schofield

Voluntary vs. Mandatory Standards

Dear Editor:

In his "Random Sampler" article, "Keep Standards Mandatory," in the February 1999 Actuarial Review, David G. Hartman, Chairman of the Actuarial Standards Board (ASB), wants to eat his cake, but preserve it at the same time. He states that Actuarial Standards of Practice is "authoritative guidance," but is not a "straightjacket." He insists that standards remain mandatory but yet... "ASOPs are already voluntary, as an actuary may choose to follow them or to disclose in what way his or her practice deviates." It is precisely this double-think that I have tried to eliminate in my call for voluntary standards ("Random Sampler," Actuarial Review, November 1998). What is the point of calling vague guidelines mandatory and then saying that if you don't like the guidelines, you can voluntarily not use them by saying you're not using them? Isn't it better to call standards voluntary and make them specific and attractive so that more and more actuaries would voluntarily want to use them?

Mr. Hartman states that "An ASOP is promulgated only after an extensive exposure process, during which comments are encouraged from all actuaries." Recently, the ASB sent out its second exposure draft on a proposed ASOP on Statements of Actuarial Opinion Regarding Property Casualty Loss and Loss Adjustment Expense Reserves. Loss reserves are the very lifeblood of actuarial science, yet how many actuaries commented on the first exposure draft? The ASB stated that 39 letters and 53 postcards were received. Out of 2,899 Associates and Fellows listed in the 1998 CAS Yearbook, that's a very unimpressive 3 percent response rate. As an aside, out of the 92 responses, three, (3 percent of the respondents) did not want an ASOP on this topic.

So why weren't actuaries interested? Perhaps the ASB product is not meaningful to them because it's not very specific or very good. Mr. Hartman suggests that "If an actuary does not like mandatory standards (to which one agrees to be bound on joining the profession), he or she can always choose to resign from the profession." I trust that Mr. Hartman is not offering the ASB as a governmental licensing mechanism for actuaries. I wonder what percentage of actuaries Mr. Hartman would like to see resign from the profession because of disagreement with mandatory standards? And what about those actuaries who entered the profession before the creation of the ASB in 1989?

I serve on the CAS Committee on Professionalism Education (COPE). In its work this past year, COPE considered how to expand its workshops on professionalism from CAS students to include all CAS members. Mandatory attendance was considered, then dropped after a membership survey. COPE decided it would try to develop a product strong enough to attract practicing actuaries.

To conclude, it seems to me that Mr. Hartman and I do not disagree over standards; we only disagree over the vehicle in which to deliver them to the profession. I recommend the ASB become a Good Actuary's Seal of Approval: issue voluntary specific standards meaningful to most actuaries. These ASB products will then effectively promote and encourage actuarial professionalism. To learn a lesson from Kevin Costner's movie, Field of Dreams: "If we build it, they will come."

Charles Gruber, FCAS

Hartman Responds

Mr. Gruber's observations miss my essential points. First, mandatory standards (to which we as a profession have collectively agreed to be bound) are the hallmark of professionalism and essential to the public confidence in the actuarial profession. Second, the Actuarial Standards of Practice appropriately allow actuaries to exercise professional judgment in their application, but disclosure of material deviations from those standards is needed if users of actuarial work products are to understand that a deviation from standards has occurred. The "voluntary standards" that Mr. Gruber advocates would not, in my opinion, be standards at all.

David G. Hartman, FCAS