Let's face it: insurance isn't known as the most trustworthy industry. According to Ernst & Young, consumer trust in insurers is at about 70 percent right now. This is less than even banks, another business often seen as dishonest.

That may explain why insurance companies have a hard time attracting millennials. Gallup.com reported millennials are the least likely to engage with insurers. And when they do buy insurance, they're more than twice as likely to do so on line. Not reassuring news for insurers, as Generation Y makes up 25 percent of the country's population.

Innovative Insurance Companies

While most companies are sticking with their standard insurance practices and existing customer bases, a few are shaking things up to cast a wider net. Some are allowing consumers to save on their rates using peer-to-peer insurance models. Others are offering increased flexibility by letting people choose exactly what they want to insure (think individual possessions at a lower cost rather than all of the possessions in your house).

Above all, these organizations have a digital-first mindset. All of the following companies have apps, and some even let you buy coverage right from your phone. Here's a list of a few firms striving to stand out from the crowd:

Lemonade

Type of Insurance: Renters, home, condo, and co-op insurance

What Makes It Unique: Lemonade is an insurance peer-to-peer (P2P) start-up. Their website says you can get coverage in 90 seconds and have your claims paid out in three minutes using their app.

A typical insurance company loses money when they pay your claim. Instead, Lemonade says they treat premiums like it's your money. The company takes a fixed 20 percent and uses the rest to pay claims. If there's leftover money, they give it to charities like Feeding America, American Red Cross, and Make-A-Wish.

“Most Americans view insurance as a necessary evil rather than a social good, and that’s something we’d like to change,” said Daniel Schreiber, Lemonade’s CEO.

The catch? Right now it's only available for New Yorkers, but Yael Wissner-Levy, director of strategic communications at Lemonade, says they're exploring options to move into different locations (and types of insurance).

Back Me Up

Type of Insurance: Personal property and travel coverage

What Makes It Unique: This UK-insurance product, backed by insurance giant Ageas, lets customers pick and choose what items they want protected. Aimed at millennials, Back Me Up only offers coverage to 18- to 49-year-olds. And like Lemonade, everything is handled through a mobile app.

According to Back Me Up's research, five million 18- to 34-year-olds don't have contents coverage. On top of that, 2.3 million don't use travel insurance when they leave the country, leaving them without coverage if they lose one of their belongings on vacation.

Despite this, millennials do value their items, particularly their cellphones and laptops. So why aren't they bothering to insure their belongings?

"[We spoke] to young, independently minded people who told us that they have not engaged with the insurance market while still thinking it key to protect certain possessions," Paul Lynes, managing director at Back Me Up, told the Post. "However, in the past, their only options were full-blown cover, or nothing. And when they did buy insurance, they were annoyed by things like penalty fees, which we have abolished."

Consumers can cover three of their most prized possessions for a fee of £15 a month. This gives them Back Me Up's "core cover," which insures three possessions no matter where you are for up to £3,000 in claims per month. You'll be eligible for one free screen repair a year on your cell phone even if it isn't one of your three covered items. If it is, you'll be able to repair it more than once.

You're also able to switch the belongings you cover as often as you want. And with no annual contract­­—just a monthly fee—you won't be locked in to anything.

Another benefit to your core coverage is locksmith services for your house and car. Back Me Up will help you get back into your home or vehicle for up to £1,500 a month. This fee also gives customers travel insurance. According to the Back Me Up website, customers have protection against lost items, cancellations, and medical emergencies.

If you're looking for more coverage, Back Me Up offers Bolt Ons including:

  • Stuff +1: Add an additional item and an extra $1,000 in coverage.
  • Landlords: Helps with legal advice against landlords. Offers legal indemnity coverage up to 50,000.
  • Breakdown: Covers your van, car, or motorcycle if it breaks down. This applies if you're a driver or passenger.
  • Adventure: Insurance for activities such as whitewater rafting and other extreme sports. Covers injuries and sports equipment.

Guevara

Type of Insurance:  Car insurance

What Makes It Unique: Guevara, a digital company based in the UK, also uses a P2P approach for car insurance. With Guevara, you pool part of your premiums with a group of other drivers to save up to 50 percent.

You'll pay a "base price" based off individual factors such as location and age. After that, you're put in a group with other drivers. The bigger your pool, the less you pay. You can either join a friend or family member's pool, or be placed in one based on your profile.

Part of your policy money goes towards the group's insurance costs. The rest of your money goes in the group's pool. You're able to pay your claims using the collective money in your pool.

Once your money runs out, the group's insurance fees cover extra expenses. If you have any money left over, it gets rolled into the pool for next year. You'll pay your insurance fees each year, as well as whatever it takes to get back to your group's original pool amount.

"Insurance is such a large proportion of household discretionary spending. By giving our customers accountability within their groups and making that transparent for everyone, we can reduce the cost of motor insurance for everyone," Rich Phillip, one of Guevara's founders, told dailyfintech.com.

Zoom+

Type of Insurance: Health insurance

What Makes It Unique: Zoom+ offers both medical care and health insurance, making it easier for healthcare providers to provide quality care at an affordable cost.

This is similar to Kaiser Permanente, which is also both a medical care provider and insurer. But unlike Kaiser, Zoom+ treats people who have Zoom+ insurance, no insurance, or other health plans. Still, not everyone can seek treatment at a Zoom+ clinic. They don't provide care to those on Medicaid or Medicare.

Currently operating only in Portland, Seattle, and Vancouver, Washington, Zoom+ is targeted at millennials who want fast and efficient care. As such, by using the Zoom+ app, customers are able to make appointments right from their phone. Appointments are often quick, sometimes half an hour or less. Zoom+ insurance members can also get care from Zoom partners like Oregon Health & Science University hospitals.

Another thing that makes Zoom+ different? They strive to avoid unnecessary tests to keep costs low, and make heavy use of nurse practitioners and physician assistants. The clinics offer additional services like dental care, mental health treatment, and even yoga and cooking classes.

Friendsurance

Type of Insurance: Liability, home, legal expenses, electronics, car, and mobile phone insurance

What Makes It Unique: The founders of German P2P insurtech company Friendsurance wanted to find a way to reward insurance customers who paid hundreds of dollars for coverage they may never use. Essentially, they wanted to compensate consumers who practiced safe behaviors, and therefore never filed a claim.

With Friendsurance, they're able to give users a cash-back bonus at the end of the year if they haven't filed a claim. Customers can receive up to 40 percent of their premiums back. This benefits the consumer, of course, but also encourages them to stay safe whether they're on the road or in their homes. It also helps to reduce fraud.

According to Friendsurance, their claim frequency is below average. In 2013 and 2014, more than 80 percent of Friendsurance customers who participated in the claims-free bonus received some of their money back.

Like Guevara, policy owners are placed into groups. Part of your premium goes into a shared pool. If there are no claims that year, you receive cash back. If there is a claim, then it's paid off by the shared pool, and the amount you receive back at the end of the year is reduced. Any amount that exceeds the pool's money is paid through the insurance company.

If you're considering using Friendsurance, note this claims-free bonus is only offered for certain insurance products including home contents, private liability, and legal expense coverage.