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Ruin probability of a two-dimensional discrete time risk model with random interest rates. (Chinese. English summary) Zbl 1399.91039

Summary: In this paper we study a two-dimensional discrete time risk model with random interest rates, which is constructed by the two-dimensional random vectors that are composed of the marginal distributions of random variables, and set up a more actual demand two-dimensional model. We study the finite-time ruin probability in this two-dimensional model by using the similar method to find the two-dimensional finite-time ruin probability in a two-dimensional discrete time risk model. Under some given assumptions, the following uniformly asymptotic result about the two-dimensional finite-time ruin probability is established by using the similar method to find the two-dimensional finite-time ruin probability in a two-dimensional discrete time risk model with constant interest rates: as \(x \to \infty \), \(\varphi \left ({x, n} \right) \sim \sum\limits_{k = 1}^n \sum\limits_{j = 1}^n {P\left ({{X_{1, k}}\mathop \Pi \limits_{l = 1}^k {Y_l} > {x_1}, {X_{2, j}}\mathop \Pi \limits_{l = 1}^k {Y_l} > {x_2}} \right)} ,\) here \(x = {x_1} + {x_2}.\) This result generalizes the corresponding result in a two-dimensional discrete time risk model with constant interest rates.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91G30 Interest rates, asset pricing, etc. (stochastic models)
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