Pricing Catastrophe Reinsurance with Reinstatement Provisions Using a Catastrophe Model
نویسندگان
چکیده
In recent years catastrophe reinsurers' use of catastrophe models has been increasing until currently virtually all of the catastrophe reinsurers in the world use a catastrophe model to aid them in their pricing and portfolio management decisions. This paper explicitly models various types of reinstatement provisions, including reinstatements that are limited by the number of occurrences and by the aggregate losses; and reinstatement premiums based on the size of loss and by the time elapsed to the first occurrence. The paper also investigates the effects on the fair premium of a catastrophe treaty when various reinstatement provisions are considered. This is an expansion of the methods developed in papers by Leroy J. Simon and Bjom Sundt, which were written before the widespread use of catastrophe models.
منابع مشابه
Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity
We use the Cox process (or a doubly stochastic Poisson process) to model the claim arrival process for catastrophic events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic Markov process theory. We apply the model to price stop-loss catastrophe reinsurance contract and catast...
متن کاملDoubly Stochastic Poisson Process and the Pricing of Catastrophe Reinsurance Contract
We use a doubly stochastic Poisson process (or the Cox process) to model the claim arrival process for catastrophic events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic Markov process theory. We apply the Cox process incorporating the shot noise process as its intensity to...
متن کاملAn Integrated Approach to Pricing Catastrophe Reinsurance
We propose an integrated approach straddling the actuarial science and the mathematical finance approaches to pricing a default-risky catastrophe reinsurance contract. We first apply an incomplete-market version of the no-arbitrage martingale pricing paradigm to price the reinsurance contract as a martingale by a measure change, then we apply risk loading to price in—as in the traditional actua...
متن کاملOptimal Dividend and Reinsurance Strategy of a Property Insurance Company under Catastrophe Risk
We consider an optimal control problem of a property insurance company with proportional reinsurance strategy. The insurance business brings in catastrophe risk, such as earthquake and flood. The catastrophe risk could be partly reduced by reinsurance. The management of the company controls the reinsurance rate and dividend payments process to maximize the expected present value of the dividend...
متن کاملImproving Risk Allocation Through Cat Bonds
Catastrophe bonds (cat bonds) often use index triggers, such as, for instance, parametric descriptions of a catastrophe. This implies the problem of the so-called basis risk, resulting from the fact that, in contrast to traditional reinsurance, this kind of coverage cannot be a perfect hedge for the primary’s insured portfolio. On the other hand, cat bonds offer some very attractive economic fe...
متن کامل