scholarly journals Probability of Ruin under Inflationary Conditions or under Experience Rating

1979 ◽  
Vol 10 (2) ◽  
pp. 149-162 ◽  
Author(s):  
G. C. Taylor
Keyword(s):  
Ruin Probability ◽  
Safety Margin ◽  
Simple Modification ◽  
Probability Of Ruin ◽  
Experience Rating ◽  
Constant Rate ◽  
Aggregate Claims ◽  
Premium Income ◽  
Rating Scheme ◽  
Made In

The effect of inflation of premium income and claims size distribution, but not of free reserves, on the probability of ruin of an insurer is studied.An interesting similarity between this problem and the ruin problem in an experience-rated scheme is exhibited. This similarity allows the deduction of parallel results for the two problems in later sections.It is shown that the probability of ruin is always increased when the (constant) inflation rate is increased.The distribution of aggregate claims under inflationary conditions is described and used to calculate an upper bound on the ruin probability. Some numerical examples show that this bound is not always sharp enough to be practically useful. It is also shown, however, that this bound can be used to construct an approximation of the effect of inflation on ruin probability.It is shown that if inflation occurs at a constant rate, then ruin is certain, irrespective of the smallness of that rate and of the largeness of initial free reserves and the safety margin in the premium. The corresponding result for experiencerated schemes is that a practical and “intuitively reasonable” experience-rating scheme leads eventually to certain ruin.Finally, a simple modification of the techniques of the paper is made in order to bring investment income into account.

Social Recourses of the Population under Conditions of Losing Economic Stability

2015 ◽  
pp. 86-99 ◽  
Author(s):  
E. Avraamova ◽  
T. Maleva
Keyword(s):  
Economic Development ◽  
Social Policy ◽  
Social Development ◽  
Safety Margin ◽  
Economic Stability ◽  
Socio Economic Development ◽  
Development Stability ◽  
Made In

The loss of country’s socio-economic development stability puts on the agenda the problem of finding solutions contributing to the maintenance of Russian households’ welfare. The authors believe that these solutions lie in the broader area than applying various instruments of monetary support. The most effective solutions are related to the actualization of own resources of households that can act as a safety margin as well as a source of social development. The attempt to evaluate the households’ resource provision and highlight the significance of each resource enabling or creating barriers to the growth of households’ welfare is made in this article. On the basis of received conclusions social policy areas directed at preserving or enhancing the welfare are defined.

scholarly journals Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 982
Author(s):  
Yujuan Huang ◽  
Jing Li ◽  
Hengyu Liu ◽  
Wenguang Yu
Keyword(s):  
Fourier Series ◽  
Ruin Probability ◽  
Risk Model ◽  
Expansion Method ◽  
Nonparametric Estimator ◽  
Insurance Risk ◽  
Numerical Examples ◽  
Complex Fourier Series ◽  
Premium Income ◽  
Insurance Risk Model

This paper considers the estimation of ruin probability in an insurance risk model with stochastic premium income. We first show that the ruin probability can be approximated by the complex Fourier series (CFS) expansion method. Then, we construct a nonparametric estimator of the ruin probability and analyze its convergence. Numerical examples are also provided to show the efficiency of our method when the sample size is finite.

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.

A finite-time ruin probability formula for continuous claim severities

2004 ◽  
Vol 41 (2) ◽  
pp. 570-578 ◽  
Author(s):  
Zvetan G. Ignatov ◽  
Vladimir K. Kaishev
Keyword(s):  
Real Function ◽  
Finite Time ◽  
Ruin Probability ◽  
Joint Distribution ◽  
Time Interval ◽  
Insurance Company ◽  
Finite Time Interval ◽  
Appell Polynomials ◽  
Premium Income ◽  
Inverted Dirichlet

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.

scholarly journals Erlangian Approximations for Finite-Horizon Ruin Probabilities

2002 ◽  
Vol 32 (2) ◽  
pp. 267-281 ◽  
Author(s):  
Soren Asmussen ◽  
Florin Avram ◽  
Miguel Usabel
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Fluid Model ◽  
Ruin Probabilities ◽  
Approximation Procedure ◽  
Exponential Form ◽  
Probability Of Ruin ◽  
Phase Type ◽  
The Matrix ◽  
The Mean

AbstractFor the Cramér-Lundberg risk model with phase-type claims, it is shown that the probability of ruin before an independent phase-type time H coincides with the ruin probability in a certain Markovian fluid model and therefore has an matrix-exponential form. When H is exponential, this yields in particular a probabilistic interpretation of a recent result of Avram & Usabel. When H is Erlang, the matrix algebra takes a simple recursive form, and fixing the mean of H at T and letting the number of stages go to infinity yields a quick approximation procedure for the probability of ruin before time T. Numerical examples are given, including a combination with extrapolation.

scholarly journals A Heuristic Review of some Ruin Theory Results

1985 ◽  
Vol 15 (2) ◽  
pp. 73-88 ◽  
Author(s):  
G. C. Taylor
Keyword(s):  
Size Distribution ◽  
Stochastic Dominance ◽  
Ruin Probability ◽  
Recursion Formula ◽  
Claim Size ◽  
Infinite Time ◽  
Ruin Theory ◽  
Interesting Connection ◽  
Claim Size Distribution ◽  
Aggregate Claims

AbstractThe paper deals with the renewal equation governing the infinite-time ruin probability. It is emphasized as intended to be no more than a pleasant ramble through a few scattered results. An interesting connection between ruin probability and a recursion formula for computation of the aggregate claims distribution is noted and discussed. The relation between danger of the claim size distribution and ruin probability is reexamined in the light of some recent results on stochastic dominance. Finally, suggestions are made as to the way in which the formula for ruin probability leads easily to conclusions about the effect on that probability of the long-tailedness of the claim size distribution. Stable distributions, in particular, are examined.

scholarly journals On the time value of absolute ruin with debit interest

2007 ◽  
Vol 39 (02) ◽  
pp. 343-359 ◽  
Author(s):  
Jun Cai
Keyword(s):  
Differential Equations ◽  
Ruin Probability ◽  
Expected Discounted Penalty Function ◽  
Surplus Process ◽  
Absolute Ruin ◽  
The Laplace Transform ◽  
The Absolute ◽  
Heavy Tailed ◽  
Premium Income ◽  
Debit Interest

Assume that the surplus of an insurer follows a compound Poisson surplus process. When the surplus is below zero or the insurer is on deficit, the insurer could borrow money at a debit interest rate to pay claims. Meanwhile, the insurer will repay the debts from her premium income. The negative surplus may return to a positive level. However, when the negative surplus is below a certain critical level, the surplus is no longer able to be positive. Absolute ruin occurs at this moment. In this paper, we study absolute ruin questions by defining an expected discounted penalty function at absolute ruin. The function includes the absolute ruin probability, the Laplace transform of the time to absolute ruin, the deficit at absolute ruin, the surplus just before absolute ruin, and many other quantities related to absolute ruin. First, we derive a system of integro-differential equations satisfied by the function and obtain a defective renewal equation that links the integro-differential equations in the system. Second, we show that when the initial surplus goes to infinity, the absolute ruin probability and the classical ruin probability are asymptotically equal for heavy-tailed claims while the ratio of the absolute ruin probability to the classical ruin probability goes to a positive constant that is less than one for light-tailed claims. Finally, we give explicit expressions for the function for exponential claims.

The calculation of the inner potential of a crystal

1951 ◽  
Vol 206 (1085) ◽  
pp. 232-241 ◽  
Keyword(s):  
Crystal Lattice ◽  
Electron Distribution ◽  
Exponential Approximation ◽  
Simple Modification ◽  
The Past ◽  
Sources Of Error ◽  
Atomic Scattering ◽  
Experimental Values ◽  
Made In

Although a number of calculations of the inner potential have been made in the past for various crystals, the results have not been entirely satisfactory, and in some cases widely divergent values for the same substance were published by different authors. In the present work, a number of these calculations are examined and possible sources of error discussed. It is shown that electron distribution charts and curves obtained experimentally are not suitable for the calculation of inner potential, and an exponential approximation for atomic scattering factors is given which is found to be more reliable for this purpose. A simple modification of the electron distribution curves obtained from these atomic scattering factors is described; this is applied when the atoms are bound in a crystal lattice, thus enabling the inner potential of the crystal to be calculated. The results of a number of calculations based on this method are given and compared with the experimental values, the agreement being satisfactory.

scholarly journals Discrete Time Ruin Probability for Takaful (Islamic Insurance) with Investment and Qard-Hasan (Benevolent Loan) Activities

2020 ◽  
Vol 13 (9) ◽  
pp. 211 ◽  
Author(s):  
Dila Puspita ◽  
Adam Kolkiewicz ◽  
Ken Seng Tan
Keyword(s):  
Business Model ◽  
Ruin Probability ◽  
Risk Model ◽  
Computational Procedure ◽  
Profit Sharing ◽  
Probability Of Ruin ◽  
Agent Based ◽  
Key Variables ◽  
Islamic Insurance ◽  
The Impact

The main objectives of this paper are to construct a new risk model for modelling the Hybrid-Takaful (Islamic Insurance) and to develop a computational procedure for calculating the associated ruin probability. Ruin probability is an important study in actuarial science to measure the level of solvency adequacy of an insurance product. The Hybrid-Takaful business model applies a Wakalah (agent based) contract for underwriting activities and Mudharabah (profit sharing) contract for investment activities. We consider the existence of qard-hasan facility provided by the operator (shareholder) as a benevolent loan for the participants’ fund in case of a deficit. This facility is a no-interest loan that will be repaid if the business generates profit in the future. For better investment management, we propose a separate investment account of the participants’ fund. We implement several numerical examples to analyze the impact of some key variables on the Takaful business model. We also find that our proposed Takaful model has a better performance than the conventional counterpart in terms of the probability of ruin.

scholarly journals Estimates for the Absolute Ruin Probability in the Compound Poisson Risk Model with Credit and Debit Interest

2008 ◽  
Vol 45 (03) ◽  
pp. 818-830 ◽  
Author(s):  
Jinxia Zhu ◽  
Hailiang Yang
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Absolute Ruin ◽  
Constant Rate ◽  
Negative Constant ◽  
The Absolute ◽  
Debit Interest ◽  
Poisson Risk Model

In this paper we consider a compound Poisson risk model where the insurer earns credit interest at a constant rate if the surplus is positive and pays out debit interest at another constant rate if the surplus is negative. Absolute ruin occurs at the moment when the surplus first drops below a critical value (a negative constant). We study the asymptotic properties of the absolute ruin probability of this model. First we investigate the asymptotic behavior of the absolute ruin probability when the claim size distribution is light tailed. Then we study the case where the common distribution of claim sizes are heavy tailed.

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