A LITTLE TIP FROM ME TO YOU, or, THAT'S WHY I LEARNED GAME THEORY: Now that my renter's insurance claim has been more-or-less resolved (the check's in the mail, as they say), a few lessons I learned from my experience:
1. Renter's insurance is totally worth it. The loss of my guitar equipment was moderate, financially--I should be able to scrape together the money to replace everything without starving--and though I got something less than the full value of everything, the check they're sending will still be for more than I've paid in renter's insurance for the past two years. If you live anyplace that has any crime to speak of, its a worthwhile investment.
2. Take photographs of anything that might be even remotely valuable. Fortunately, I was playing around with my digital camera a few months ago, and happened to take up-close pictures of my acoustic guitar, which went a long way to demonstrating I owned it. The process of documenting ownership, particularly if, like me, you've never thought of it before, is tedious and aggravating--an ounce of prevention and all that.
3. If possible, pay more to have a lower deductible. I'm not sure what the marginal cost of a lower deductible is, but it's almost certainly worth it, especially if you're a grad student with limited financial resources. A lower cost now beats a higher cost at a moment you're not expecting.
4. Information asymmetries are a wonderful thing. As a Ron Paul supporter might say, DO your HOMEWORK. In a lovely game-theoretic fashion, the insurance company is trying to find the point at which you're willing to settle (reservation point?), and they will start on the low end. The check will be for slightly more than double their original offer, largely because 1. I knew some relevant facts they did not (the acoustic guitar I had stolen was a model that hasn't been made for over 30 years; they should've known this, since I included that information in the documentation I sent to them, but it was clear the adjuster had done a cursory read, at best) 2. I know a little bit about how depreciation works, which allowed me to argue it was not applicable for some of the things I lost (I could've continued fighting on this one and gotten more, I think, but it wasn't worth the hassle to me)* 3. Recognizing that the squeaky wheel gets the grease. After giving a week and a half for them to work on my claim, I started calling every day, leaving messages if I didn't get through, and respectfully but firmly arguing my case when I thought they were being unfair. In so doing, I signaled that I was willing to continue until I got a fair value for the items I had stolen, at which point it becomes easier for them to make me a better offer rather than have me arguing discount rates with them for a week.
*Actually, a pet theory I've developed over the past few weeks: I think the depreciation for most guitar-related items is zero, or else negative (and thus increasing in value over time), the only exceptions being things with a processor. What drives down the price of a number of items in the 5-15 year range is the presence of a large secondary market, and their close similarity to guitars and amps as they're made today (that is, the value of my 12-year old guitar is similar to the same guitar made today, but since I could go out and buy a new guitar for the same price, its value is discounted in the secondary market).