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The paper deals with a generalization of the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. First of all, we derive piecewise integro-differential equations for the Gerber--Shiu…
The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by…
We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model…
The Gerber-Shiu function is a classical research topic in actuarial science.However, exact solutions are only available in the literature for very specific cases where the claim amounts follow distributions such as the exponential…
We consider in this paper a risk reserve process where the claims and gains arrive according to two independent Poisson processes. While the gain sizes are phase-type distributed, we assume instead that the claim sizes are phase-type…
Our paper explores a discrete-time risk model with time-varying premiums, investigating two types of correlated claims: main claims and by-claims. Settlement of the by-claims can be delayed for one time period, representing real-world…
We consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains $C_i$ ($i=1,2,\dots$) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model…
In this paper we develop the Gerber-Shiu theory for the classic and dual discrete risk processes in a Markovian (regime switching) environment. In particular, by expressing the Gerber-Shiu function in terms of potential measures of an…
We consider a discrete-time dividend payout problem with risk sensitive shareholders. It is assumed that they are equipped with a risk aversion coefficient and construct their discounted payoff with the help of the exponential premium…
Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate the ultimate ruin probability in the Gerber-Dickson risk model is provided when claims follow a negative binomial mixture distribution. The…
The Gerber-Shiu function provides a unified framework for the evaluation of a variety of risk quantities. Ever since its establishment, it has attracted constantly increasing interests in actuarial science, whereas the conventional research…
The article presents a general discrete time dividend valuation model when the dividend growth rate is a general continuous variable. The main assumption is that the dividend growth rate follows a discrete time semi-Markov chain with…
This paper concerns an optimal dividend distribution problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process (in the absence of dividend payments). The management of the company is assumed to…
The Gerber-Shiu function provides a way of measuring the risk of an insurance company. It is given by the expected value of a function that depends on the ruin time, the deficit at ruin, and the surplus prior to ruin. Its computation…
The discrete time risk model with two seasons and dependent claims is considered. An algorithm is created for computing the values of the ultimate ruin probability. Theoretical results are illustrated with numerical examples.
This paper concerns an optimal dividend distribution problem for an insurance company with surplus-dependent premium. In the absence of dividend payments, such a risk process is a particular case of so-called piecewise deterministic Markov…
The paper investigates a discrete time Binomial risk model with different types of polices and shock events may influence some of the claim sizes. It is shown that this model can be considered as a particular case of the classical compound…
We consider a discrete-time version of the popular optimal dividend pay-out problem in risk theory. The novel aspect of our approach is that we allow for a risk averse insurer, i.e., instead of maximising the expected discounted dividends…
In this manuscript we consider the dual risk model with financial application, where the random gains occur under a renewal process. We particularly work the Erlang(n) case for common distribution of the inter-arrival times, from there it…
This paper considers an insurance surplus process modeled by a spectrally negative L\'{e}vy process. Instead of the time of ruin in the traditional setting, we apply the time of drawdown as the risk indicator in this paper. We study the…