Is there any empirical evidence that women are more likely to engage
in risk taking behavior during the luteal phase of their menstrual
cycle?

Here is my speculation. From an evolutionary perspective, during the
luteal phase, a woman ovulates. This is the period where she needs to
select the father of her child. More risk taking might translate into
a wider selection of mates, and hence more fit offsprings
(statistically speaking). Empirical literature from anthropology,
sociology, psychology and medicine might touch this issue. All I seem
to be able to find from the medical literature is research comparing
mood changes between sportswomen and sedatory women. That is not what
I need.

Being a 47 year old woman, I can certainly see why you are asking this
interesting question.  Having had a tubal ligation after 2 kids at age
28, I have had 20 years of sexual activity unemcumbered by the fear of
pregnancy.

Men deal with constant testosterone, women on the other hand, are
flooded with hormones at different intervals throughout each month. 
Looking back, I have undeniably been MUCH more prone to risky sexual
behavior around the time I ovulate.  I have even noticed that it is
around the time I ovulate.  There have been times I look back at my
behavior aand wonder "What was I THINKING?"  I guess the answer is: I
WASN'T THINKING.

No, you are not asking about simple mood swings.  I know exactly what
you are asking about.  I bet there are more women out there that have
noticed this.  Maybe others will post.  Hopefully someone can find
some studies for you.

~~Cynthia