Asymptotics for the finite-time ruin probability in a discrete-time risk model with dependent insurance and financial risks*

Consider a discrete-time insurance risk model with risky investments. Under the assumption that the loss distribution belongs to a certain subclass of the subexponential class, Tang and Tsitsiashvili (Stochastic Processes and Their Applications 108(2): 299–325 (2003)) established a precise estimate for the finite time ruin probability. This article extends the result both to the whole subexponential class and to a nonstandard case with associated discount factors.

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The Finite-Time Ruin Probability with Dependent Insurance and Financial Risks

Journal of Applied Probability ◽

10.1017/s0021900200008603 ◽

2011 ◽

Vol 48 (04) ◽

pp. 1035-1048 ◽

Cited By ~ 10

Author(s):

Yiqing Chen

Keyword(s):

Finite Time ◽

Ruin Probability ◽

Risk Model ◽

Domain Of Attraction ◽

Random Variable ◽

Distribution Functions ◽

Financial Risks ◽

Finite Time Ruin Probability ◽

Special Cases ◽

Maximum Domain Of Attraction

Consider a discrete-time insurance risk model. Within periodi, the net insurance loss is denoted by a real-valued random variableXi. The insurer makes both risk-free and risky investments, leading to an overall stochastic discount factorYifrom timeito timei− 1. Assume that (Xi,Yi),i∈N, form a sequence of independent and identically distributed random pairs following a common bivariate Farlie-Gumbel-Morgenstern distribution with marginal distribution functionsFandG. WhenFis subexponential andGfulfills some constraints in order for the product convolution ofFandGto be subexponential too, we derive a general asymptotic formula for the finite-time ruin probability. Then, for special cases in whichFbelongs to the Fréchet or Weibull maximum domain of attraction, we improve this general formula to be transparent.

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Ruin probability analysis in geometric inhomogeneous claims case

Lietuvos matematikos rinkinys ◽

10.15388/lmr.2011.ot01 ◽

2011 ◽

Vol 52 ◽

Author(s):

Eugenija Bieliauskienė

Keyword(s):

Discrete Time ◽

Finite Time ◽

Ruin Probability ◽

Risk Model ◽

Geometric Distribution ◽

Probability Analysis ◽

Finite Time Ruin Probability

The discrete time risk model with inhomogeneous claims is analyzed. The finite time ruin probability expression is obtained for the case when claims are distributed by geometric distribution with changing parameters. Some quantitave examples are also given.

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The Finite-Time Ruin Probability with Dependent Insurance and Financial Risks

Journal of Applied Probability ◽

10.1239/jap/1324046017 ◽

2011 ◽

Vol 48 (4) ◽

pp. 1035-1048 ◽

Cited By ~ 29

Author(s):

Yiqing Chen

Keyword(s):

Finite Time ◽

Ruin Probability ◽

Risk Model ◽

Domain Of Attraction ◽

Random Variable ◽

Distribution Functions ◽

Financial Risks ◽

Finite Time Ruin Probability ◽

Special Cases ◽

Maximum Domain Of Attraction

Consider a discrete-time insurance risk model. Within period i, the net insurance loss is denoted by a real-valued random variable Xi. The insurer makes both risk-free and risky investments, leading to an overall stochastic discount factor Yi from time i to time i − 1. Assume that (Xi, Yi), i ∈ N, form a sequence of independent and identically distributed random pairs following a common bivariate Farlie-Gumbel-Morgenstern distribution with marginal distribution functions F and G. When F is subexponential and G fulfills some constraints in order for the product convolution of F and G to be subexponential too, we derive a general asymptotic formula for the finite-time ruin probability. Then, for special cases in which F belongs to the Fréchet or Weibull maximum domain of attraction, we improve this general formula to be transparent.

Download Full-text