Measures of risk for the classical risk process using saddlepoint approximation techniques

2012 ◽  
Author(s):  
Benjamin Baumgartner
Keyword(s):  
Saddlepoint Approximation ◽  
Risk Process ◽  
Approximation Techniques ◽  
Measures Of Risk ◽  
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.

The Asymptotic Distributions Of Some Test Statistics in Near-Integrated AR Processes

1995 ◽  
Vol 11 (2) ◽  
pp. 306-330 ◽  
Author(s):  
Rolf Larsson
Keyword(s):  
Saddlepoint Approximation ◽  
Distribution Functions ◽  
Asymptotic Distributions ◽  
Test Statistics ◽  
Approximation Techniques

Asymptotic distributions of some test statistics in near-integrated AR processes are studied. Some exact formulas for the distribution functions are given as well as approximative results obtained by saddlepoint approximation techniques.

scholarly journals Optimal Investment and Bounded Ruin Probability: Constant Portfolio Strategies and Mean-variance Analysis

2008 ◽  
Vol 38 (2) ◽  
pp. 423-440 ◽  
Author(s):  
Ralf Korn ◽  
Anke Wiese
Keyword(s):  
Expected Utility ◽  
Ruin Probability ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Risk Process ◽  
Investment Strategies ◽  
Portfolio Strategies ◽  
Classical Risk Process ◽  
Portfolio Optimization Problem ◽  
Mean Variance

We study the continuous-time portfolio optimization problem of an insurer. The wealth of the insurer is given by a classical risk process plus gains from trading in a risky asset, modelled by a geometric Brownian motion. The insurer is not only interested in maximizing the expected utility of wealth but is also concerned about the ruin probability. We thus investigate the problem of optimizing the expected utility for a bounded ruin probability. The corresponding optimal strategy in various special classes of possible investment strategies will be calculated. For means of comparison we also calculate the related mean-variance optimal strategies.

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