This dissertation introduces a game theoretic modeling framework and a series of models to examine the interactions between the key stakeholders (property owners, insurers, reinsurers and government) of a natural catastrophe insurance market, which possesses a complicated structure and faces many challenges from the natural catastrophe loss. Specifically, we integrate (1) a utility-based homeowner decision model; (2) a stochastic optimization model to optimize reinsurance decision by the primary insurer(s); (3) a heuristic government intervention model to reduce uninsured losses through price support for insurance purchase and acquisition; and (4) a state-ofthe-art regional catastrophe loss estimation model, all within the framework of a static Cournot-Nash noncooperative game assuming perfect information. We allow the number of primary insurers to increase from one (monopoly) to many (oligopoly) within the Cournot-Nash framework, and examines the impacts of competition on market performance from each stakeholder's perspective. An automatic ResponseSurface and Trust-Region algorithm is developed to solve the models for real, regional applications. A case study for residential wood frame buildings in Eastern North Carolina is presented. The case study suggests that: (a) private insurance market competition is an efficient mechanism to reduce uninsured loss, which should be facilitated by government; (b) more competition challenges insurers but benefits homeowners, and there exists a balance between insurer profitability and insurance penetration; (c) acquisition, price support and encouraging insurers to keep catastrophe reserve can all improve market performance and reduce uninsured loss; and (d) catastrophe reserves should be encouraged, which not only help insurers to avoid insolvency, but could also limit competition if imposed as barrier of entry, thus improve their profitability.