Policies typically use vague language when referring to acts of terrorism, but they are generally insured by the comprehensive portion of your policy. For example, if there is an act of terror and you need to make a claim on your car, that can only be made if you have comprehensive coverage. Since some circumstances are out of our control, comprehensive insurance is certainly important to have in your policy.
Muslim scholars have varying opinions about life insurance. Life insurance policies that earn interest (or guaranteed bonus/NAV) are generally considered to be a form of riba (usury) and some consider even policies that do not earn interest to be a form of gharar (speculation). Some argue that gharar is not present due to the actuarial science behind the underwriting. Jewish rabbinical scholars also have expressed reservations regarding insurance as an avoidance of God's will but most find it acceptable in moderation.
Formal self-insurance is the deliberate decision to pay for otherwise insurable losses out of one's own money. This can be done on a formal basis by establishing a separate fund into which funds are deposited on a periodic basis, or by simply forgoing the purchase of available insurance and paying out-of-pocket. Self-insurance is usually used to pay for high-frequency, low-severity losses. Such losses, if covered by conventional insurance, mean having to pay a premium that includes loadings for the company's general expenses, cost of putting the policy on the books, acquisition expenses, premium taxes, and contingencies. While this is true for all insurance, for small, frequent losses the transaction costs may exceed the benefit of volatility reduction that insurance otherwise affords.
Let's use the aftermath of a major storm to illustrate the differences between collision and comprehensive. Within that storm, let's consider two hypothetical events: First, a heavy telephone pole was blown down and fell on your truck, or second, you swerved to avoid a falling tree and wound up crashing into a guardrail. In the first event, you couldn't control when or why a tree fell on your car. This kind of accident would get reimbursed under your comprehensive policy. In the second situation, you were driving the car and ultimately swerved into the guardrail. This makes it a collision, and collision insurance pays for the damages.