Here's the deal:
Standard homeowner's insurance (this also includes renter's policies) covers the "named insured's" (check your policy to see who is a "named insured"...dependent kids away from home are considered a "named insured") personal contents and possessions for a variety of "named perils" (theft is a "named peril") if the loss takes place either at the "insured premises" or at other locations away from the insured premises (like while on vacation, at school, and so on).
Deductible $ amounts are chosen at the time the policy is purchased...the higher your deductible the less you have to pay. This works like your auto collision deductible, appies to all first party losses (your bike is stolen). Deductibles do not apply for third party losses (liability claims....like when your pit bull mauls the neighbor's 5 yr. old kid when he tries to touch your cool bike).
Most losses are adjusted and settled at the "actual cash value" (ACV) of the item at the time of the loss, which takes depreciation of the item into consideration. Note to hipsters: insurance companies depreciate used converted fixed bikes heavily ("you want how much for that old, single speed, POS with no brakes?").
If you choose the "replacement cost" option when buying the policy, then the damaged/stolen items will be valued at the current cost to replace with like kind and quality. This means keep all the receipts for all that blingy crap you've put on your bike.
Most homeowners policies have built in $ limits for a variety of types of property (jewelry, electronics, cameras, bikes, etc.). these limits are clearly stated on the policy....always read your contract. Most people never do, and this benefits the insurance thieves.
If you have a lot of possessions with a value in excess of "these stated policy limits" for certain items (like that custom made ti Seven with all the DA stuff on it, or Grandma's 12 ct. diamond ring) then you can add these items, "schedule them", on a "policy rider". This can either establish a higher limit for the particular class of property in general, or it gives a "stated value" for the particular item in question (like your $10K one-of-a-kind fixie with collector's spoke cards, Jackson Pollock spatter paint job, designer hemp top tube protector and Prada silk bandana).
And, yes, it you file a claim you'll likely be cancelled by the insurance thieves. I know all this because I used to work for The Shifting Sands Property and Casualty Insurance Company.