scholarly journals Upper Bound of Ruin Probability for an Insurance Discrete-Time Risk Model with Proportional Reinsurance and Investment

2018 ◽  
Vol 14 (3) ◽  
pp. 595 ◽  
Author(s):  
Apichart Luesamai ◽  
Samruam Chongcharoen
Keyword(s):  
Discrete Time ◽  
Upper Bound ◽  
Ruin Probability ◽  
Risk Model ◽  
Proportional Reinsurance

scholarly journals Dynamic Proportional Reinsurance and Approximations for Ruin Probabilities in the Two-Dimensional Compound Poisson Risk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Yan Li ◽  
Guoxin Liu
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Optimal Strategies ◽  
Proportional Reinsurance ◽  
Two Dimensional ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman ◽  
Poisson Risk Model

We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds and the Cramér-Lundberg approximation for the ruin probability and show that as the capital tends to infinity, the optimal strategies converge to the asymptotically optimal constant strategies. The asymptotic value can be found by maximizing the adjustment coefficient.

scholarly journals Minimizing an Insurer’s Ultimate Ruin Probability by Reinsurance and Investments

2019 ◽  
Vol 24 (1) ◽  
pp. 21 ◽  
Author(s):  
Christian Kasumo
Keyword(s):  
Integral Equation ◽  
Ruin Probability ◽  
Stock Price ◽  
Risk Model ◽  
Vital Role ◽  
Insurance Companies ◽  
Claim Amount ◽  
Proportional Reinsurance ◽  
Investment Return ◽  
Return Process

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard a Black–Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton–Jacobi–Bellman (HJB) approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed individual claim amount distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.

scholarly journals Ruin Probabilities of a Discrete-time Multi-risk Model

2015 ◽  
Vol 44 (4) ◽  
pp. 367-379 ◽  
Author(s):  
Andrius Grigutis ◽  
Agneška Korvel ◽  
Jonas Šiaulys
Keyword(s):  
Discrete Time ◽  
Ruin Probability ◽  
Arrival Time ◽  
Risk Model ◽  
Recursive Formula ◽  
Ruin Probabilities ◽  
Numerical Examples ◽  
Premium Rate ◽  
Insurance Business ◽  
Independent Series

In this work,  we investigate a  multi-risk model describing insurance business with  two or more independent series of claim amounts. Each series of claim amounts consists of independent nonnegative random variables. Claims of each series occur periodically with some fixed   inter-arrival time. Claim amounts occur until they   can be compensated by a common premium rate and the initial insurer's surplus.  In this article, wederive a recursive formula for calculation of finite-time ruin probabilities. In the case of bi-risk model, we present a procedure to calculate the ultimate ruin probability. We add several numerical examples illustrating application  of the derived formulas.DOI: http://dx.doi.org/10.5755/j01.itc.44.4.8635

scholarly journals Infinite time ruin probability in inhomogeneous claims case

2010 ◽  
Vol 51 ◽  
Author(s):  
Eugenija Bieliauskienė ◽  
Jonas Šiaulys
Keyword(s):  
Discrete Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Recursive Formula ◽  
Infinite Time

The article deals with the classical discrete-time risk model with non-identically distributed claims. The recursive formula of infinite time ruin probability is obtained, which enables to evaluate the probability to ruin with desired accuracy.

scholarly journals A Dependent Insurance Risk Model with Surrender and Investment under the Thinning Process

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Wenguang Yu ◽  
Yujuan Huang
Keyword(s):  
Interest Rates ◽  
Upper Bound ◽  
Ruin Probability ◽  
Risk Model ◽  
Arrival Process ◽  
Insurance Risk ◽  
Martingale Theory ◽  
Thinning Process ◽  
First Time ◽  
Insurance Risk Model

A dependent insurance risk model with surrender and investment under the thinning process is discussed, where the arrival of the policies follows a compound Poisson-Geometric process, and the occurrences of the claim and surrender happen as the p-thinning process and the q-thinning process of the arrival process, respectively. By the martingale theory, the properties of the surplus process, adjustment coefficient equation, the upper bound of ruin probability, and explicit expression of ruin probability are obtained. Moreover, we also get the Laplace transformation, the expectation, and the variance of the time when the surplus reaches a given level for the first time. Finally, various trends of the upper bound of ruin probability and the expectation and the variance of the time when the surplus reaches a given level for the first time are simulated analytically along with changing the investment size, investment interest rates, claim rate, and surrender rate.

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