Related papers: Ruin problems for risk processes with dependent ph…
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 start by showing that the finite-time absolute ruin probability in the classical risk model with constant interest force can be expressed in terms of the transition probability of a positive Ornstein-Uhlenbeck type process, say X. Our…
We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant…
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…
We consider a classical risk process with arrival of claims following a non-stationary Hawkes process. We study the asymptotic regime when the premium rate and the baseline intensity of the claims arrival process are large, and claim size…
We study a general perturbed risk process with cumulative claims modelled by a subordinator with finite expectation, with the perturbation being a spectrally negative Levy process with zero expectation. We derive a Pollaczek-Hinchin type…
In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cram\'er--Lundberg reserve process having absolutely continuous but otherwise general claim size distributions. We employ a dense…
Predicting future operational risk losses gives rise to a significant challenge due to the heterogeneous and time-dependent structures present in real-world data. Furthermore, stress test exercises require examining the relationship with…
The embedding problem of Markov transition matrices into continuous-time Markov semigroups is a classic problem that regained a lot of impetus and activities in recent years. We consider it here for the following generalisation of the…
A phase-type distribution is the distribution of the time until absorption in a finite state-space time-homogeneous Markov jump process, with one absorbing state and the rest being transient. These distributions are mathematically tractable…
In this paper we investigate continuity properties for ruin probability in the classical risk model. Properties of contractive integral operators are used to derive continuity estimates for the deficit at ruin. These results are also…
We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an…
We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution…
In this paper we propose new iterative algorithm of calculating the joint distribution of the Parisian ruin time and the number of claims until Parisian ruin for the classical risk model. Examples are provided when the generic claim size is…
In this paper, we study a risk process modeled by a Brownian motion with drift (the diffusion approximation model). The insurance entity can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin.…
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…
We study the problem of learning Markov decision processes with finite state and action spaces when the transition probability distributions and loss functions are chosen adversarially and are allowed to change with time. We introduce an…
In the design of probabilistic timed systems, bounded requirements concerning behaviour that occurs within a given time, energy, or more generally cost budget are of central importance. Traditionally, such requirements have been…
In this paper we consider the classical and Erlang(2) risk processes when the inter-claim times and claim amounts are dependent. We assume that the dependence structure is defined through a Farlie-Gumbel-Morgenstern (FGM) copula and show…
We consider a $d-$dimensional insurance network, with initial capital $a\in\R^d_+,$ operating under a risk diversifying treaty; this is described in terms of a regulated random walk $\{Z^{(a)}_n\}$ via Skorokhod problem in $\R^d_+$ with…