Yes, and voluntarily — with any lawful insurer, or with an international agency.
Insurance is treated as the investor’s own commercial decision — the law states that insurance of investments and of investors’ risks is voluntary — and then sets out what a political-risk policy is expected to answer for: requisition or expropriation of property and any legislative or administrative measure leading to its seizure or alienation or to a loss of control over it or over the income it produces; the introduction of restrictions on transferring foreign currency out of the country; interference by state bodies and their officials in investors’ contractual relations; war and civil unrest; and other political risks. (Investment Law, Arts. 21, 50 — lex.uz ↗)
Cover may be taken from any insurance organisation lawfully operating in Uzbekistan, and equally from international organisations, foreign agencies and other insurance companies. The law is careful about who stands behind what: insurers do not answer for the obligations of Uzbekistan, and the state does not answer for the obligations of insurers except where an agreement between the parties says so. (Investment Law, Art. 50 — lex.uz ↗)
Accounting keeps the books and makes every filing on time, with monthly reports in English.
Part of the answer bank — 195 questions, each cited to the article it rests on.