Ruin Problems of Multidimensional Risk Models under Constant Interest Rates and Dependent Risks with Heavy Tails

Xinmei Shen,Dawei Lu,Meng Yuan

doi:10.1155/2020/9489612

Xinmei Shen, Dawei Lu + Show 1 more

Open Access

https://doi.org/10.1155/2020/9489612

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Abstract

Consider a discrete-time multidimensional risk model with constant interest rates where capital transfers between lines are partially allowed over each period. By assuming a large initial capital and regularly varying distributions for the losses, we derive asymptotic estimates for the ruin probability under some dependence structure and study the optimal allocation of the initial reserve. Some numerical simulations are provided to illuminate our main results.

Highlights

Consider an insurer with multiple business lines against catastrophic risks. e eventual occurrence of these events usually has a substantial effect on some lines of business simultaneously.us, the statistical dependence among claims in these business lines should be considered
Under the framework of heavy-tailed and nonidentically distributed claim sizes with some dependence structure, Li et al [13] focused on the finite-time ruin probability of the continuous-time multidimensional model in which capital transfers were partially allowed, and they studied the optimal allocation of the initial reserve
Under the assumption that the claim size vector follows a multivariate regularly varying distribution, capital transfers between business lines are partially allowed with different fractions 􏼈ωi ∈ [0, 1], i 1, . . . , d􏼉 for each line

Summary

Introduction

Consider an insurer with multiple business lines against catastrophic risks (e.g., earthquakes, floods, hurricane, or terrorist attacks). e eventual occurrence of these events usually has a substantial effect on some lines of business simultaneously. Huang et al [12] considered a discrete-time multidimensional risk model with the assumption of regularly varying distribution for net losses and established asymptotic estimates for finitetime ruin probabilities in terms of the upper tail dependence function. Under the framework of heavy-tailed and nonidentically distributed claim sizes with some dependence structure, Li et al [13] focused on the finite-time ruin probability of the continuous-time multidimensional model in which capital transfers were partially allowed, and they studied the optimal allocation of the initial reserve. Under the assumption that the claim size vector follows a multivariate regularly varying distribution, capital transfers between business lines are partially allowed with different fractions 􏼈ωi ∈ [0, 1], i 1, .

Multidimensional Finite-Time Ruin Probability

Initial Reserve Allocation

Numerical Studies