RUIN PROBABILITY FOR HYPO-EXPONENTIAL CLAIM IN CLASSICAL RISK PROCESS WITH REINSURANCE

2019 ◽  
Vol 20 (1) ◽  
pp. 37-51
Author(s):  
Khanchit Chuarkham ◽  
Arthit Intarasit ◽  
Pakwan Riyapan
Keyword(s):  
Ruin Probability ◽  
Risk Process ◽  
Classical Risk Process

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.

Ruin probabilities for competing claim processes

2004 ◽  
Vol 41 (03) ◽  
pp. 679-690 ◽  
Author(s):  
Miljenko Huzak ◽  
Mihael Perman ◽  
Hrvoje Šikić ◽  
Zoran Vondraček
Keyword(s):  
Ruin Probability ◽  
Lévy Process ◽  
Risk Process ◽  
Levy Process ◽  
Ruin Probabilities ◽  
Classical Risk Process ◽  
Risk Processes

Let C 1, C 2,…,C m be independent subordinators with finite expectations and denote their sum by C. Consider the classical risk process X(t) = x + ct - C(t). The ruin probability is given by the well-known Pollaczek–Khinchin formula. If ruin occurs, however, it will be caused by a jump of one of the subordinators C i . Formulae for the probability that ruin is caused by C i are derived. These formulae can be extended to perturbed risk processes of the type X(t) = x + ct - C(t) + Z(t), where Z is a Lévy process with mean 0 and no positive jumps.

Calculating Continuous Time Ruin Probabilities for a Large Portfolio with Varying Premiums

2009 ◽  
Vol 39 (1) ◽  
pp. 117-136 ◽  
Author(s):  
Lourdes B. Afonso ◽  
Alfredo D. Egídio dos Reis ◽  
Howard R. Waters
Keyword(s):  
Gamma Distribution ◽  
Continuous Time ◽  
Finite Time ◽  
Ruin Probability ◽  
Numerical Evaluation ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Aggregate Claims ◽  
Classical Risk Process ◽  
Major Consideration

AbstractIn this paper we present a method for the numerical evaluation of the ruin probability in continuous and finite time for a classical risk process where the premium can change from year to year. A major consideration in the development of this methodology is that it should be easily applicable to large portfolios. Our method is based on the simulation of the annual aggregate claims and then on the calculation of the ruin probability for a given surplus at the start and at the end of each year. We calculate the within-year ruin probability assuming a translated gamma distribution approximation for aggregate claim amounts.We illustrate our method by studying the case where the premium at the start of each year is a function of the surplus level at that time or at an earlier time.

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

2008 ◽  
Vol 38 (02) ◽  
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.

Ruin probabilities for competing claim processes

2004 ◽  
Vol 41 (3) ◽  
pp. 679-690 ◽  
Author(s):  
Miljenko Huzak ◽  
Mihael Perman ◽  
Hrvoje Šikić ◽  
Zoran Vondraček
Keyword(s):  
Ruin Probability ◽  
Lévy Process ◽  
Risk Process ◽  
Levy Process ◽  
Ruin Probabilities ◽  
Classical Risk Process ◽  
Risk Processes

LetC1,C2,…,Cmbe independent subordinators with finite expectations and denote their sum byC. Consider the classical risk processX(t) =x+ct-C(t). The ruin probability is given by the well-known Pollaczek–Khinchin formula. If ruin occurs, however, it will be caused by a jump of one of the subordinatorsCi. Formulae for the probability that ruin is caused byCiare derived. These formulae can be extended to perturbed risk processes of the typeX(t) =x+ct-C(t) +Z(t), whereZis a Lévy process with mean 0 and no positive jumps.

Expansions for Markov-modulated systems and approximations of ruin probability

1996 ◽  
Vol 33 (01) ◽  
pp. 57-70
Author(s):  
Bartłomiej Błaszczyszyn ◽  
Tomasz Rolski
Keyword(s):  
Ruin Probability ◽  
Marked Point ◽  
Factorial Moment ◽  
Risk Process ◽  
Rate Function ◽  
Marked Point Process ◽  
Probability Of Ruin ◽  
Actual Risk ◽  
Moment Measures ◽  
Markov Modulated

Let N be a stationary Markov-modulated marked point process on ℝ with intensity β ∗ and consider a real-valued functional ψ(N). In this paper we study expansions of the form Eψ(N) = a 0 + β ∗ a 1 + ·· ·+ (β∗ ) nan + o((β ∗) n ) for β ∗→ 0. Formulas for the coefficients ai are derived in terms of factorial moment measures of N. We compute a 1 and a 2 for the probability of ruin φ u with initial capital u for the risk process in the Markov-modulated environment; a 0 = 0. Moreover, we give a sufficient condition for ϕu to be an analytic function of β ∗. We allow the premium rate function p(x) to depend on the actual risk reserve.

scholarly journals A Lévy Insurance Risk Process with Tax

2008 ◽  
Vol 45 (02) ◽  
pp. 363-375 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Jean-François Renaud ◽  
Xiaowen Zhou
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Risk Process ◽  
Fluctuation Theory ◽  
Insurance Risk ◽  
Exit Problem ◽  
Tax Payments ◽  
Aggregate Income

Using fluctuation theory, we solve the two-sided exit problem and identify the ruin probability for a general spectrally negative Lévy risk process with tax payments of a loss-carry-forward type. We study arbitrary moments of the discounted total amount of tax payments and determine the surplus level to start taxation which maximises the expected discounted aggregate income for the tax authority in this model. The results considerably generalise those for the Cramér-Lundberg risk model with tax.

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