scholarly journals Measuring Durability of Insurance Company Based on Ruin Probability

2020 ◽  
Vol 17 ◽  
Keyword(s):  
Exponential Distribution ◽  
Discrete Time ◽  
Ruin Probability ◽  
Claim Size ◽  
Limited Time ◽  
Insurance Company ◽  
Probability Of Ruin ◽  
Initial Capital ◽  
The Given

In this paper, we present the process of the measuring durability of insurance company, in which, this study focus on the discrete-time under the limited time the company must reserve sufficient initial capital to ensure that probability of ruin does not exceed the given quantity of risk. Therefore the illustration of the minimum initial capital under the specified period for the claim size process to the exponential distribution has explained.

scholarly journals The probability of ruin in a reinsurance risk model with m-dependence assumptions

2021 ◽  
Author(s):  
HOANG NGUYEN HUY ◽  
NGUYEN CHUNG
Keyword(s):  
Discrete Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Random Variables ◽  
Upper Bounds ◽  
Insurance Company ◽  
Probability Of Ruin ◽  
Numerical Example ◽  
Surplus Process ◽  
Inductive Methods

In this article, we investigate a discrete-time risk model. The risk model includes the quota- (α,β) reinsurance contract effect on the surplus process. The premium process and claim process are assumed to be m-dependent sequences of i.i.d. non-negative random variables. Using Martingale and inductive methods, we obtain upper bounds for ultimate ruin probability of an insurance company. Finally, we present a numerical example to show the efficiency of the methods.

scholarly journals Ruin probability with certain stationary stable claims generated by conservative flows

2007 ◽  
Vol 39 (02) ◽  
pp. 360-384 ◽  
Author(s):  
Uğur Tuncay Alparslan ◽  
Gennady Samorodnitsky
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Ruin Probability ◽  
Stable Process ◽  
Independent Interest ◽  
Stable Processes ◽  
Auxiliary Result ◽  
Initial Capital ◽  
Order Of Magnitude

We study the ruin probability where the claim sizes are modeled by a stationary ergodic symmetric α-stable process. We exploit the flow representation of such processes, and we consider the processes generated by conservative flows. We focus on two classes of conservative α-stable processes (one discrete-time and one continuous-time), and give results for the order of magnitude of the ruin probability as the initial capital goes to infinity. We also prove a solidarity property for null-recurrent Markov chains as an auxiliary result, which might be of independent interest.

The impact of time discretization on solvency measurement

2017 ◽  
Vol 18 (1) ◽  
pp. 2-20 ◽  
Author(s):  
Hato Schmeiser ◽  
Daliana Luca
Keyword(s):  
Discrete Time ◽  
Risk Measures ◽  
Time Discretization ◽  
Capital Requirements ◽  
Insurance Company ◽  
Probability Of Ruin ◽  
Content Type ◽  
The One ◽  
Discretization Interval ◽  
The Impact

Purpose The purpose of this paper is to study how the discretization interval affects the solvency measurement of a property-liability insurance company. Design/methodology/approach Starting with a basic solvency model, the authors study the impact of the discretization interval on risk measures. The analysis considers the sensitivity of the discrepancy between the risk measures in continuous and discrete time to various parameters, such as the asset-to-liability ratio, the characteristics of the asset and liability processes, as well as the correlation between assets and liabilities. Capital requirements for the one-year planning horizon in continuous vs discrete time are reported as well. The purpose is to report the degree to which the deviations in risk measures, due to the different discretization intervals, can be reduced by means of increasing the frequency with which the risk measures are assessed. Findings The simulation results suggest that the risk measures of an insurance company are consistently underestimated when assessed on an annual basis (as it is currently done under insurance regulation such as Solvency II). The authors complement the analysis with the capital requirements of an insurance company and conclude that more frequent discretization translates into higher capital requirements for the insurance company. Both the probability of ruin and the expected policyholder deficit (EPD) can be reduced through intermediate financial reports. Originality/value The results from our simulation analysis suggest that that the choice of discretization interval has an impact on the risk assessment of an insurance company which uses the probability of ruin and the EPD as risk measures. By assessing the risk measures once a year, both risk measures and the capital requirements are consistently underestimated. Therefore, the recommendation for risk managers is to complement the capital requirements in solvency regulation with sensitivity analyses of the risk measures presented with respect to time discretization. On the one hand, it seems to us that there is value in knowing about the substantial discrepancy between the focused time discrete ruin probability and EPD compared to the continuous version. On the other hand, and if there are no substantial transaction costs associated with more frequent monitoring of solvency figures, a frequent update would be helpful to increase the accuracy of the calculations and reduce the EPD.

scholarly journals Ruin probability with certain stationary stable claims generated by conservative flows

2007 ◽  
Vol 39 (2) ◽  
pp. 360-384 ◽  
Author(s):  
Uğur Tuncay Alparslan ◽  
Gennady Samorodnitsky
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Ruin Probability ◽  
Stable Process ◽  
Independent Interest ◽  
Stable Processes ◽  
Auxiliary Result ◽  
Initial Capital ◽  
Order Of Magnitude

We study the ruin probability where the claim sizes are modeled by a stationary ergodic symmetric α-stable process. We exploit the flow representation of such processes, and we consider the processes generated by conservative flows. We focus on two classes of conservative α-stable processes (one discrete-time and one continuous-time), and give results for the order of magnitude of the ruin probability as the initial capital goes to infinity. We also prove a solidarity property for null-recurrent Markov chains as an auxiliary result, which might be of independent interest.

Optimal Risk Control for The Excess of Loss Reinsurance Policies

2010 ◽  
Vol 40 (1) ◽  
pp. 179-197 ◽  
Author(s):  
Hui Meng ◽  
Xin Zhang
Keyword(s):  
Ruin Probability ◽  
Risk Control ◽  
Optimal Level ◽  
Primary Objective ◽  
Management Tool ◽  
Insurance Company ◽  
Probability Of Ruin ◽  
Black Scholes ◽  
Reinsurance Treaty ◽  
Riskless Asset

AbstractThe primary objective of the paper is to explore using reinsurance as a risk management tool for an insurance company. We consider an insurance company whose surplus can be modeled by a Brownian motion with drift and that the surplus can be invested in a risky or riskless asset. Under the above Black-Scholes type framework and using the objective of minimizing the ruin probability of the insurer, we formally establish that the excess-of-loss reinsurance treaty is optimal among the class of plausible reinsurance treaties. We also obtain the optimal level of retention as well as provide an explicit expression of the minimal probability of ruin.

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 A class of risk processes with delayed claims: ruin probability estimates under heavy tail conditions

2006 ◽  
Vol 43 (4) ◽  
pp. 916-926 ◽  
Author(s):  
Ayalvadi Ganesh ◽  
Giovanni Luca Torrisi
Keyword(s):  
Size Distribution ◽  
Ruin Probability ◽  
Heavy Tail ◽  
Claim Size ◽  
Probability Estimates ◽  
Claim Size Distribution ◽  
Risk Processes

We consider a class of risk processes with delayed claims, and we provide ruin probability estimates under heavy tail conditions on the claim size distribution.

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