In this paper we consider the probabilities of finiteand infinite-time absolute ruin in the renewal risk model with constant premium rate and constant force of interest. In the particular case of compound Poisson model, explicit asymptotic expressions for the finiteand infinite-time absolute ruin probabilities are given. For the general renewal risk model, we present an asymptotic expression fo...

We are interested in statistical inference for the finite-time ruin probability of an insurance surplus whose claim process has a long-range dependence. As an approximated model, we consider a surplus driven by a fractional Brownian motion with the Hurst parameter H > 1/2. We can compute the ruin probability via the Monte Carlo simulations if some unknown parameters in the model are decided. Fr...

For the continuous-time risk model with compound Poisson input, the ((nite-horizont) joint probability P (t; X x; Y y) of ruin time , surplus X just before ruin and deecit Y at ruin time is considered as a function of the arrival rate of claims. It is expanded into a Taylor series at = 0. A certain extension of a corresponding result for innnite-horizont joint probabilities, which previously ha...

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...

This paper proposes a discrete-time risk model that has a centain type of correlation between premiums and claim amounts. It is motivated by the well-known No Claims Discount system or bonus-malus system 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 a...

We study a discrete-time interaction risk model with delayed claims within the framework of the compound binomial model. Using the technique of generating functions, we derive both a recursive formula and a defective renewal equation for the expected discounted penalty function. As applications, the probabilities of ruin and the joint distributions of the surplus one period to ruin and the defi...

In this paper we consider an optimal dividend problem for an insurance company which risk process evolves as a spectrally negative Lévy process (in the absence of dividend payments). We assume that the management of the company controls timing and size of dividend payments. The objective is to maximize the sum of the expected cumulative discounted dividends received until the moment of ruin and...