One possible way of risk management for an insurance company is to develop an early and appropriate alarm system before the possible ruin. The ruin is defined through the status of the aggregate risk process, which in turn is determined by premium accumulation as well as claim settlement outgo...

In this paper, we consider a risk model which allows the insurer to partially reflect the recent claim experience in the determination of the next period’s premium rate. In a ruin context, similar mechanisms to the one proposed in this paper have been studied by, e.g., Tsai and Parker (2004),...

An insurance risk model where claims follow a Markovian arrival process (MArP) is considered in this paper. It is shown that the expected present value of total operating costs up to default H, as a generalization of the classical Gerber–Shiu function, contains more non-trivial quantities than...

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 and then find the integro-differential equations...

The present paper aims to revisit the homogeneous risk model investigated by De Vylder and Goovaerts (1999, 2000). First, a claim arrival process is defined on a fixed time interval by assuming that the arrival times satisfy an order statistic property. Then, the variability and the covariance...

In this paper, we propose a nonparametric estimator for the ruin probability in a spectrally negative Lévy risk model based on low-frequency observation. The estimator is constructed via the Fourier transform of the ruin probability. The convergence rates of the estimator are studied for large...

Ruin capital is a function of premium rate set to render the probability of ruin within finite time equal to a given value. The analytical studies of this function in the classical Lundberg model of risk with exponential claim sizes done in Malinovskii (2014) have shown that the ruin capital’s...

Consider a continuous-time renewal risk model, in which the claim sizes and inter-arrival times form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. Suppose that the surplus is invested in a portfolio whose return follows a Lévy...

This paper considers a bidimensional renewal risk model with constant interest force and dependent subexponential claims. Under the assumption that the claim size vectors form a sequence of independent and identically distributed random vectors following a common bivariate...

In this paper, we consider a risk process with the arrival of claims modelled by a dynamic contagion process, a generalisation of the Cox process and Hawkes process introduced by Dassios and Zhao (2011). We derive results for the infinite horizon model that are generalisations of the...