An idea for future TWIA finance

Although they may thoroughly disagree on the direction in which reform should go, almost everyone agrees has come to agree with what I predicted in 2009:  TWIA finances are in serious need of reform.  This blog entry sketches out one direction in which TWIA might proceed.  The idea here is that TWIA should, in a steady state, have enough cash on hand in its catastrophe reserve fund to pay for insured losses and operating expenses, without having to borrow, with a high probability, say 99%.  Further TWIA should have borrowing capacity to address the rare situations (say 1% of years) in which its reserves would be inadequate. Those borrowings should be repaid by some percentage of TWIA policyholders, persons living on the coast, and Texans generally, perhaps collected through the proxy of insurers doing business in Texas.

Although people can quarrel about the precise parameters in this abstract statement of the goal, I have some hope that people could agree on the concept. Government-sponsored insurance companies that don’t have the right to draw on the government fisc, ought not to be relying heavily on post-event bonding as a way of paying claims; instead they need enough money in their piggy bank just as we require of their private insurer counterparts. But what if TWIA’s catastrophe reserve fund does not meet this lofty goal?  What then?  Especially given the magnitude of the current reserve shortfall and the current economy, matters can not be corrected overnight. There should, I say, be an adjustment period during which premiums are adjusted (either upwards or, at some hypothetical future time, downwards) such that, at the end of the adjustment period, things come into balance and the catastrophe reserve fund meets the goal.

How do we operationalize this idea? Here is the beginning of a statutory draft. I’ve put in dummy statute section numbers for ease of reference. Obviously, the real section numbers would have to be revised by legislative counsel. Also, we’re probably going to have to develop a more comprehensive process for 2210.355A(b)(1) and reconcile this provision with the alternative process currently set form in 2210.355A.


(a) Definitions

(1)  The “Exceedance Function for the catastrophe year” is a function that approximates the probability that insured lossses and operating expenses in the catastrophe year will exceed a specified dollar amount. Insured losses shall be computed on a net basis after consideration of any reinsurance or other sources of recovery.

(2) The term “Loss PDF” means the probability distribution function mathematically associated with the Exceedance Function.

(3) The term “Century Storm Reserve Adequacy” means having a catastrophe reserve fund at the start of each catastrophe year such that this fund would be able, without additional borrowing, to fully pay insured losses and operating expenses in the following catastrophe year with a 99% probability as computed using the Exceedance Function for the catastrophe year.

(4) The term “Reserve Adjustment Period” means ten years.


(1) The Association shall, prior to the start of each catastrophe year, use the best historical and scientific modeling evidence with considerations of standards in the business of catastrophe insurance, to determine the Exceedance Function and associated Loss PDF for the catastrophe year.”

(2) If, at any time, the Association finds that its catastrophe reserve fund at the start of a catastrophe year does not achieve Century Storm Reserve Adequacy,  the Association shall adjust the premiums to be charged in the following year either downwards of upwards as appropriate such that, were:

(A) such premiums to be charged for the Reserve Adjustment Period on the base of currently insured properties;

(B) insured losses and operating expenses of the Association to be for the Reserve Adjustment Period at the mean of the Loss PDF for the catastrophe year; and

(C) the Association were to earn on any reserve balances during the Reserve Adjustment Period the amount of interest for reasonably safe investments then available to the Association,

the catastrophe reserve fund at the end of Reserve Adjustment Period would achieve Century Storm Reserve Adequacy.

(c) By way of illustration, if the Exceedance Function takes on a value of 0.01 when the size of insured losses and operating expenses is a equal to 440 million dollars and the mean of the Loss PDF for the catastrophe year is equal to 223 million, the initial balance of the catastrophe reserve fund is 100 million dollars and the amount of interest for safe investments then available to the Association is equal to 2% compounded continuously, then the premiums charged for the following calendar year should be equal to $614,539,421.

And what happens, by the way, if a storm hits that exceeds the size of the catastrophe reserve fund?  Stay tuned.  I’ve got an idea there too.

How do we keep premiums low under this scheme?  Likewise, stay tuned.  Hint: think about coinsurance requirements and lower maximum policy limits.  Think about carrots to get the private insurance industry writing excess policies on the coast with ever lower attachment points.

  • Footnote for math nerds only. Anyone seeing the implicit differential equations in the model and the applications of control theory?
  • Footnote for Mathematica folks only. Here’s the program to compute the premium. Note the use of polymorphic functions.

p[\[Omega]_, \[Mu]_, q_, c_, r_, z_] :=
x /. First@
Solve[Quantile[\[Omega], q] ==
TimeValue[c, EffectiveInterest[r, 0], z] +
TimeValue[Annuity[x – \[Mu], z], EffectiveInterest[r, 0], z],
p[\[Omega]_, q_, c_, r_, z_] :=
With[{m = NExpectation[x, x \[Distributed] \[Omega]]},
p[\[Omega], \[Mu], q, c, r, z]]

  • Footnote for statutory drafters. Note the use of modular drafting such that one can change various parameters in the scheme (such as the 10 year adjustment period) without having to redraft the whole statute.