Computing the Probability of Eventual Ruin
نویسنده
چکیده
Shiu derives two formulas for calculating the probability of eventual ruin in a collective risk model. This paper implements one of the formulas by incorporating an algorithm to reduce round-off error due to convolution. It gives the results of the programs for some claim distributions. The usefulness of these two formulas is also discussed.
منابع مشابه
Asymptotics for the infinite time ruin probability of a dependent risk model with a constant interest rate and dominatedly varying-tailed claim sizes
This paper mainly considers a nonstandard risk model with a constant interest rate, where both the claim sizes and the inter-arrival times follow some certain dependence structures. When the claim sizes are dominatedly varying-tailed, asymptotics for the infinite time ruin probability of the above dependent risk model have been given.
متن کاملSelf-annuitization and Ruin in Retirement
At retirement, most individuals face a choice between voluntary annuitization and discretionary management of assets with systematic withdrawals for consumption purposes. Annuitization— buying a life annuity from an insurance company—assures a lifelong consumption stream that cannot be outlived, but it is at the expense of a complete loss of liquidity. On the other hand, discretionary managemen...
متن کاملInsurance Risk with Variable Number of Policies
In this paper we consider an insurance company selling life insurance policies. New policies are sold at random points in time, and each policy stays active for a random amount of time, during which the policyholder pays premiums continuously at rate r. When the policy expires, the insurance company pays a claim of random size. The aim is to compute the probability of eventual ruin starting wit...
متن کاملOn a discrete-time two level NCD risk model
This paper proposes a discrete-time NCD risk model that incorporates the well-known No Claims Discount (NCD) system (or bonus-malus system (BMS)) in the car insurance industry. Such a system penalises policyholders at fault in accidents by surcharges, and rewards claim-free years by discounts. For simplicity, only two levels of premium are considered in the given model and recursive formulae ar...
متن کاملOn the Time Value of Absolute Ruin with Debit Interest
Assume that the surplus of an insurer follows a compound Poisson surplus process. When the surplus is below zero or the insurer is on deficit, the insurer could borrow money at a debit interest rate to pay claims. Meanwhile, the insurer will repay debts from her premium income. The negative surplus may return to a positive level if debts are reasonable. However, when the negative surplus is bel...
متن کامل