I am a math instructor self studying for the actuarial exam and I am trying to understand the following notation that I have encountered today.
$$E[X \land d]$$
The explanation in the book told me that this means
$$E[\min\{X,d\}]$$
which is another unfamiliar notation to me.
Just guessing from what I have learned I want to say that this is related to reimbursements with deductibles with $X$ being the loss which I learned it as
$$E[Y]$$ while $$Y = \begin{cases} 0, & x<d\\ x-d, & x\ge d \end{cases}$$
Am I in the right ball park or does it mean something completely different? It would be great if you could guide me to where I can learn about this a bit more because I do not even know how it is read.
This notation isn't particular to actuaries (see here). $\wedge$ means the minimum. Dually, $\vee$ would mean maximum.
$E(f(x))=\int f(x)p(x) \mathrm{d}x$ by definition.
Thus you get
$E(\min(X,d)) = \int \min(x,d)p(x) \mathrm{d}x$
$\min(X,d)$ means "take $X$ if $X < d$, otherwise take $d$."
Another notation you may come across (particularly for max) is $(S_T - K)^+ = \max(S_T-K,0)$ which is the payoff of a call option.