scholarly journals Tail probability of a random sum with a heavy-tailed random number and dependent summands

2015 ◽  
Vol 432 (1) ◽  
pp. 504-516 ◽  
Author(s):  
Fengyang Cheng
Keyword(s):  
Random Number ◽  
Tail Probability ◽  
Random Sum ◽  
Heavy Tailed

Large deviations of heavy-tailed random sums with applications in insurance and finance

1997 ◽  
Vol 34 (2) ◽  
pp. 293-308 ◽  
Author(s):  
C. Klüppelberg ◽  
T. Mikosch
Keyword(s):  
Distribution Function ◽  
Large Deviation ◽  
Random Variables ◽  
Compound Poisson Process ◽  
Random Sum ◽  
Random Sums ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Heavy Tailed ◽  
The Right

We prove large deviation results for the random sum , , where are non-negative integer-valued random variables and are i.i.d. non-negative random variables with common distribution function F, independent of . Special attention is paid to the compound Poisson process and its ramifications. The right tail of the distribution function F is supposed to be of Pareto type (regularly or extended regularly varying). The large deviation results are applied to certain problems in insurance and finance which are related to large claims.

Large deviations of heavy-tailed random sums with applications in insurance and finance

1997 ◽  
Vol 34 (02) ◽  
pp. 293-308 ◽  
Author(s):  
C. Klüppelberg ◽  
T. Mikosch
Keyword(s):  
Distribution Function ◽  
Large Deviation ◽  
Random Variables ◽  
Compound Poisson Process ◽  
Random Sum ◽  
Random Sums ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Heavy Tailed ◽  
The Right

We prove large deviation results for the random sum , , where are non-negative integer-valued random variables and are i.i.d. non-negative random variables with common distribution function F, independent of . Special attention is paid to the compound Poisson process and its ramifications. The right tail of the distribution function F is supposed to be of Pareto type (regularly or extended regularly varying). The large deviation results are applied to certain problems in insurance and finance which are related to large claims.

An expansion for the distribution function of a random sum

1973 ◽  
Vol 10 (4) ◽  
pp. 869-874 ◽  
Author(s):  
L. M. Marsh
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Special Form ◽  
Edgeworth Expansion ◽  
Random Number ◽  
Probability Generating Function ◽  
Random Variables ◽  
Fixed Number ◽  
Random Sum

The Edgeworth expansion gives an indication of the rate of convergence of the distribution function of the sum of a fixed number of random variables to the normal distribution. A similar expansion is given here for the distribution function of the sum of a random number N of random variables, when the probability generating function of N takes a special form.

A note on the max-sum equivalence of randomly weighted sums of heavy-tailed random variables

2013 ◽  
Vol 18 (4) ◽  
pp. 519-525 ◽  
Author(s):  
Yang Yang ◽  
Kaiyong Wang ◽  
Remigijus Leipus ◽  
Jonas Šiaulys
Keyword(s):  
Random Variables ◽  
Tail Probability ◽  
Weighted Sums ◽  
Asymptotic Formulas ◽  
Dependence Structure ◽  
Insurance Risk ◽  
Risk Models ◽  
Randomly Weighted Sums ◽  
Random Weights ◽  
Heavy Tailed

This paper investigates the asymptotic behavior for the tail probability of the randomly weighted sums ∑k=1nθkXk and their maximum, where the random variables Xk and the random weights θk follow a certain dependence structure proposed by Asimit and Badescu [1] and Li et al. [2]. The obtained results can be used to obtain asymptotic formulas for ruin probability in the insurance risk models with discounted factors.

scholarly journals Uniform Asymptotics for Discounted Aggregate Claims in Dependent Risk Models

2014 ◽  
Vol 51 (3) ◽  
pp. 669-684 ◽  
Author(s):  
Yang Yang ◽  
Kaiyong Wang ◽  
Dimitrios G. Konstantinides
Keyword(s):  
Lévy Process ◽  
Tail Probability ◽  
Levy Process ◽  
Insurance Company ◽  
Risk Models ◽  
Heavy Tailed Distributions ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Heavy Tailed ◽  
Renewal Risk

In this paper we consider some nonstandard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim size distribution belongs to some classes of heavy-tailed distributions and a constraint is imposed on the Lévy process in terms of its Laplace exponent, we obtain some asymptotic formulae for the tail probability of discounted aggregate claims and ruin probabilities holding uniformly for some finite or infinite time horizons.

Approximations of value-at-risk as an extreme quantile of a random sum of heavy-tailed random variables

2015 ◽  
Vol 10 (2) ◽  
pp. 1-21 ◽  
Author(s):  
Lincoln Hannah ◽  
Borek Puza
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Random Variables ◽  
Random Sum ◽  
Extreme Quantile ◽  
Heavy Tailed

VaR Approximation: Random Sum of Heavy Tailed Distributions

2014 ◽  
Author(s):  
Lincoln Hannah
Keyword(s):  
Random Sum ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed

An expansion for the distribution function of a random sum

1973 ◽  
Vol 10 (04) ◽  
pp. 869-874 ◽  
Author(s):  
L. M. Marsh
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Special Form ◽  
Edgeworth Expansion ◽  
Random Number ◽  
Probability Generating Function ◽  
Random Variables ◽  
Fixed Number ◽  
Random Sum

The Edgeworth expansion gives an indication of the rate of convergence of the distribution function of the sum of a fixed number of random variables to the normal distribution. A similar expansion is given here for the distribution function of the sum of a random number N of random variables, when the probability generating function of N takes a special form.

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