scholarly journals Upper bounds for ruin probabilities in an autoregressive risk model with a Markov chain interest rate

2006 ◽  
Vol 2 (2) ◽  
pp. 165-175 ◽  
Author(s):  
Lin Xu ◽  
◽  
Rongming Wang
Keyword(s):  
Markov Chain ◽  
Interest Rate ◽  
Risk Model ◽  
Upper Bounds ◽  
Ruin Probabilities

scholarly journals On Joint Ruin Probabilities of a Two-Dimensional Risk Model with Constant Interest Rate

2013 ◽  
Vol 50 (02) ◽  
pp. 309-322 ◽  
Author(s):  
Zechun Hu ◽  
Bin Jiang
Keyword(s):  
Interest Rate ◽  
Differential Equations ◽  
Finite Time ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Two Dimensional ◽  
Asymptotic Expressions ◽  
Integral Differential Equations ◽  
Constant Interest Rate ◽  
Constant Interest

In this note we consider the two-dimensional risk model introduced in Avram, Palmowski and Pistorius (2008) with constant interest rate. We derive the integral-differential equations of the Laplace transforms, and asymptotic expressions for the finite-time ruin probabilities with respect to the joint ruin times T max(u 1,u 2) and T min(u 1,u 2) respectively.

scholarly journals On Joint Ruin Probabilities of a Two-Dimensional Risk Model with Constant Interest Rate

2013 ◽  
Vol 50 (2) ◽  
pp. 309-322 ◽  
Author(s):  
Zechun Hu ◽  
Bin Jiang
Keyword(s):  
Interest Rate ◽  
Differential Equations ◽  
Finite Time ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Two Dimensional ◽  
Asymptotic Expressions ◽  
Integral Differential Equations ◽  
Constant Interest Rate ◽  
Constant Interest

In this note we consider the two-dimensional risk model introduced in Avram, Palmowski and Pistorius (2008) with constant interest rate. We derive the integral-differential equations of the Laplace transforms, and asymptotic expressions for the finite-time ruin probabilities with respect to the joint ruin times Tmax(u1,u2) and Tmin(u1,u2) respectively.

Ruin Probability in a Generalised Risk Process under Rates of Interest with Homogenous Markov Chains

2014 ◽  
Vol 4 (3) ◽  
pp. 283-300
Author(s):  
Phung Duy Quang
Keyword(s):  
Markov Chain ◽  
Ruin Probability ◽  
Risk Process ◽  
Upper Bounds ◽  
Ruin Probabilities ◽  
Countable Number ◽  
Probability Inequalities ◽  
Homogenous Markov Chain ◽  
Recursive Equations ◽  
Risk Processes

AbstractThis article explores recursive and integral equations for ruin probabilities of generalised risk processes, under rates of interest with homogenous Markov chain claims and homogenous Markov chain premiums. We assume that claim and premium take a countable number of non-negative values. Generalised Lundberg inequalities for the ruin probabilities of these processes are derived via a recursive technique. Recursive equations for finite time ruin probabilities and an integral equation for the ultimate ruin probability are presented, from which corresponding probability inequalities and upper bounds are obtained. An illustrative numerical example is discussed.

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

2009 ◽  
Vol 46 (01) ◽  
pp. 99-112 ◽  
Author(s):  
Maikol A. Diasparra ◽  
Rosario Romera
Keyword(s):  
Markov Chain ◽  
Interest Rate ◽  
Discrete Time ◽  
Ruin Probability ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Proportional Reinsurance ◽  
Rate Process ◽  
Stationary Policy ◽  
The Interest Rate

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.

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