Ruin probabilities for discrete time risk models with stochastic rates of interest

In this paper we consider a discrete-time risk model, which allows the premium to be adjusted according to claims experience. This model is inspired by the well-known bonus-malus system in the non-life insurance industry. Two strategies of adjusting periodic premiums are considered: aggregate claims or claim frequency. Recursive formulae are derived to compute the finite-time ruin probabilities, and Lundberg-type upper bounds are also derived to evaluate the ultimate-time ruin probabilities. In addition, we extend the risk model by considering an external Markovian environment in which the claims distributions are governed by an external Markov process so that the periodic premium adjustments vary when the external environment state changes. We then study the joint distribution of premium level and environment state at ruin given ruin occurs. Two numerical examples are provided at the end of this paper to illustrate the impact of the initial external environment state, the initial premium level and the initial surplus on the ruin probability.

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DISCRETE TIME RISK MODELS UNDER RATES OF INTEREST

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964802163030 ◽

2002 ◽

Vol 16 (3) ◽

pp. 309-324 ◽

Cited By ~ 16

Author(s):

Jun Cai

Keyword(s):

Discrete Time ◽

Upper Bounds ◽

Ruin Probabilities ◽

Risk Models ◽

Recursive Techniques

Two discrete time risk models under rates of interest are introduced. Ruin probabilities in the two risk models are discussed. Stochastic inequalities for the ruin probabilities are derived by martingales and renewal recursive techniques. The inequalities can be used to evaluate the ruin probabilities as upper bounds. Numerical illustrations for these results are given.

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Ruin probabilities in perturbed risk models

Insurance Mathematics and Economics ◽

10.1016/s0167-6687(98)00011-0 ◽

1998 ◽

Vol 22 (1) ◽

pp. 93-104 ◽

Cited By ~ 23

Author(s):

Sabine Schlegel

Keyword(s):

Ruin Probabilities ◽

Risk Models

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On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment

Astin Bulletin ◽

10.1017/s0515036100004785 ◽

1984 ◽

Vol 14 (1) ◽

pp. 23-43 ◽

Cited By ~ 67

Author(s):

Jean-Marie Reinhard

Keyword(s):

Risk Model ◽

Risk Process ◽

Ruin Probabilities ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Risk Models ◽

Markovian Environment ◽

Necessary And Sufficient ◽

Natural Way ◽

Quantities Of Interest

AbstractWe consider a risk model in which the claim inter-arrivals and amounts depend on a markovian environment process. Semi-Markov risk models are so introduced in a quite natural way. We derive some quantities of interest for the risk process and obtain a necessary and sufficient condition for the fairness of the risk (positive asymptotic non-ruin probabilities). These probabilities are explicitly calculated in a particular case (two possible states for the environment, exponential claim amounts distributions).

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