论文信息 - Bounds for the Ruin Probability of a Discrete-Time Risk Process

Bounds for the Ruin Probability of a Discrete-Time Risk Process

We consider a discrete-time risk process driven by proportional reinsurance and an interest rate process. We assume that the interest rate process behaves as a Markov chain. To reduce the risk of ruin, we may reinsure a part or even all of the reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a stationary policy. To illustrate these results, a numerical example is included.

Rosario Romera | R. Romera | Maikol A. Diasparra | Maikol Diasparra

[1] J. Grandell. Aspects of Risk Theory , 1991 .

[2] O. Hernández-Lerma,et al. Discrete-time Markov control processes , 1999 .

[3] Jun Cai. Ruin Probabilities with Dependent Rates of Interest , 2022 .

[4] Gordon E. Willmot,et al. Lundberg approximations for compound distributions with insurance applications , 2001 .

[5] Manfred Schäl,et al. On Discrete-Time Dynamic Programming in Insurance: Exponential Utility and Minimizing the Ruin Probability , 2004 .

[6] Juan González-Hernández,et al. Markov control processes with randomized discounted cost , 2007, Math. Methods Oper. Res..

[7] Michael Taksar,et al. Stochastic Control in Insurance , 2010 .

[8] Jun Cai,et al. Ruin probabilities with a Markov chain interest model , 2004 .

[9] O. Hernández-Lerma,et al. Markov chains and invariant probabilities , 2003 .

[10] Tomasz Rolski,et al. Lundberg Approximations for Compound Distributions With Insurance Applications , 2002 .

[11] O. Hernández-Lerma,et al. Further topics on discrete-time Markov control processes , 1999 .