Ruin theory for classical risk process that is perturbed by diffusion with risky investments

2009 ◽  
Vol 25 (1) ◽  
pp. 33-44 ◽  
Author(s):  
Xiang Lin
Keyword(s):  
Risk Process ◽  
Ruin Theory ◽  
Classical Risk Process

On a modification of the classical risk process

2007 ◽  
Vol 41 (1) ◽  
pp. 156-162 ◽  
Author(s):  
M.S. Bratiychuk ◽  
D. Derfla
Keyword(s):  
Risk Process ◽  
Classical Risk Process

DYNAMIC MEAN-VARIANCE OPTIMIZATION UNDER CLASSICAL RISK MODEL WITH FRACTIONAL BROWNIAN MOTION PERTURBATION

2008 ◽  
Vol 11 (04) ◽  
pp. 589-602 ◽  
Author(s):  
HUAYUE ZHANG ◽  
LIHUA BAI
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Risk Model ◽  
Efficient Frontier ◽  
Optimal Investment ◽  
Risk Process ◽  
Classical Risk Model ◽  
Classical Risk Process ◽  
Optimal Investment Problem ◽  
Mean Variance

In this paper, we apply the completion of squares method to study the optimal investment problem under mean-variance criteria for an insurer. The insurer's risk process is modelled by a classical risk process that is perturbed by a standard fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). By virtue of an auxiliary process, the efficient strategy and efficient frontier are obtained. Moreover, when H → 1/2+ the results converge to the corresponding (known) results for standard Brownian motion.

Spectrally negative Lévy processes with applications in risk theory

2001 ◽  
Vol 33 (1) ◽  
pp. 281-291 ◽  
Author(s):  
Hailiang Yang ◽  
Lianzeng Zhang
Keyword(s):  
Lévy Processes ◽  
Compound Poisson Process ◽  
Risk Process ◽  
Levy Processes ◽  
Point Of View ◽  
Ruin Time ◽  
Classical Risk Process ◽  
Risk Processes ◽  
First Time ◽  
Spectrally Negative Lévy Processes

In this paper, results on spectrally negative Lévy processes are used to study the ruin probability under some risk processes. These processes include the compound Poisson process and the gamma process, both perturbed by diffusion. In addition, the first time the risk process hits a given level is also studied. In the case of classical risk process, the joint distribution of the ruin time and the first recovery time is obtained. Some results in this paper have appeared before (e.g., Dufresne and Gerber (1991), Gerber (1990), dos Reis (1993)). We revisit them from the Lévy process theory's point of view and in a unified and simple way.

scholarly journals Fourier/Laplace Transforms and Ruin Probabilities

2002 ◽  
Vol 32 (1) ◽  
pp. 91-105 ◽  
Author(s):  
Fátima D.P. Lima ◽  
Jorge M.A. Garcia ◽  
Alfredo D. Egídio Dos Reis
Keyword(s):  
Classical Model ◽  
Risk Process ◽  
Laplace Transforms ◽  
Ruin Probabilities ◽  
Ruin Theory ◽  
Easy Method ◽  
Arrival Times ◽  
The Real ◽  
Renewal Risk ◽  
Risk Processes

AbstractIn this paper we use Fourier/Laplace transforms to evaluate numerically relevant probabilities in ruin theory as an application to insurance. The transform of a function is split in two: the real and the imaginary parts. We use an inversion formula based on the real part only, to get the original function.By using an appropriate algorithm to compute integrals and making use of the properties of these transforms we are able to compute numerically important quantities either in classical or non-classical ruin theory. As far as the classical model is concerned the problems considered have been widely studied. In what concerns the non-classical model, in particular models based on more general renewal risk processes, there is still a long way to go. In either case the approach presented is an easy method giving good approximations for reasonable values of the initial surplus.To show this we compute numerically ruin probabilities in the classical model and in a renewal risk process in which claim inter-arrival times have an Erlang(2) distribution and compare to exact figures where available. We also consider the computation of the probability and severity of ruin in the classical model.

Ruin Theory for the Risk Process Described by PDMPs

2003 ◽  
Vol 19 (1) ◽  
pp. 59-70 ◽  
Author(s):  
Guo-jing Wang ◽  
Chun-sheng Zhang ◽  
Rong Wu
Keyword(s):  
Risk Process ◽  
Ruin Theory
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