Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 5

ruin probability Related Abstracts

5 A Hyperexponential Approximation to Finite-Time and Infinite-Time Ruin Probabilities of Compound Poisson Processes

Authors: Amir T. Payandeh Najafabadi


This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.

Keywords: heavy-tailed distributions, ruin probability, compound poisson processes, mixture exponential (hyperexponential) distribution

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4 Quantum Mechanics Approach for Ruin Probability

Authors: Ahmet Kaya


Incoming cash flows and outgoing claims play an important role to determine how is companies’ profit or loss. In this matter, ruin probability provides to describe vulnerability of the companies against ruin. Quantum mechanism is one of the significant approaches to model ruin probability as stochastically. Using the Hamiltonian method, we have performed formalisation of quantum mechanics < x|e-ᵗᴴ|x' > and obtained the transition probability of 2x2 and 3x3 matrix as traditional and eigenvector basis where A is a ruin operator and H|x' > is a Schroedinger equation. This operator A and Schroedinger equation are defined by a Hamiltonian matrix H. As a result, probability of not to be in ruin can be simulated and calculated as stochastically.

Keywords: Quantum Mechanics, ruin probability, Hamiltonian technique, operator approach

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3 Quantum Mechanism Approach for Non-Ruin Probability and Comparison of Path Integral Method and Stochastic Simulations

Authors: Ahmet Kaya


Quantum mechanism is one of the most important approaches to calculating non-ruin probability. We apply standard Dirac notation to model given Hamiltonians. By using the traditional method and eigenvector basis, non-ruin probability is found for several examples. Also, non-ruin probability is calculated for two different Hamiltonian by using the tensor product. Finally, the path integral method is applied to the examples and comparison is made for stochastic simulations and path integral calculation.

Keywords: Quantum Physics, Hamiltonian system, tensor product, ruin probability, path integral

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2 Quality of the Ruin Probabilities Approximation Using the Regenerative Processes Approach regarding to Large Claims

Authors: Safia Hocine, Djamil Aissani


Risk models, recently studied in the literature, are becoming increasingly complex. It is rare to find explicit analytical relations to calculate the ruin probability. Indeed, the stability issue occurs naturally in ruin theory, when parameters in risk cannot be estimated than with uncertainty. However, in most cases, there are no explicit formulas for the ruin probability. Hence, the interest to obtain explicit stability bounds for these probabilities in different risk models. In this paper, we interest to the stability bounds of the univariate classical risk model established using the regenerative processes approach. By adopting an algorithmic approach, we implement this approximation and determine numerically the bounds of ruin probability in the case of large claims (heavy-tailed distribution).

Keywords: Stability, risk model, ruin probability, heavy-tailed distribution, large claims, regenerative process

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1 Performance of the Strong Stability Method in the Univariate Classical Risk Model

Authors: Safia Hocine, Zina Benouaret, Djamil A¨ıssani


In this paper, we study the performance of the strong stability method of the univariate classical risk model. We interest to the stability bounds established using two approaches. The first based on the strong stability method developed for a general Markov chains. The second approach based on the regenerative processes theory . By adopting an algorithmic procedure, we study the performance of the stability method in the case of exponential distribution claim amounts. After presenting numerically and graphically the stability bounds, an interpretation and comparison of the results have been done.

Keywords: risk model, ruin probability, regenerative process, Marcov chain, strong stability

Procedia PDF Downloads 150