Well, the safest place I am on a weekly basis with private security, and the second is my home, and finally a mall with private security; not only that, they have the best price to performance ratios of places I am in. The worst price to performance ratios, and places I am most likely to be subject to violence are in fact those run by the police. I could thus argue that we would all be safer if private entities controlled all property and were responsible for safety. So, the need for the investment is omnipresent, but the person collecting, the effectiveness, the price, and morality of the situation are all subject to being better when provides by the market.

There are a few key issues people start to question like this, who funds the courts, who defends the border, who regulates food and drugs. I can assure you that there are answers for all of those to be found in the market as a series of services, contracts, bilateral agreements and the such; most of these you already engage in already without even quite realizing it. When you pick up a pair of ANSI safety goggles or buy kosher food for instance, those are private regulatory agencies that ensure the quality of the product. Many contracts already outline private arbitration, because settling things in court is aweful; if you have an issue with a product you order for instance, the company does not rely on government arbitration to refund or replace your purchase.

Honestly, the burden of proof should be on the people advocating violent expropriation, but here's a decent place to start anyway: https://mises.org/library/economics-and-ethics-private-property-0

If you have more specific topics in mind, let me know, and I'll send you some more resources. Society really doesn't require violent expropriation.