scholarly journals The maximum surplus before ruin in a jump-diffusion insurance risk process with dependence

2019 ◽  
Vol 24 (7) ◽  
pp. 3037-3050
Author(s):  
Wuyuan Jiang ◽  
Keyword(s):  
Jump Diffusion ◽  
Risk Process ◽  
Insurance Risk ◽  
Surplus Before Ruin

scholarly journals A reinsurance risk model with a threshold coverage policy: the Gerber–Shiu penalty function

2017 ◽  
Vol 54 (1) ◽  
pp. 267-285 ◽  
Author(s):  
Onno J. Boxma ◽  
Esther Frostig ◽  
David Perry
Keyword(s):  
Risk Model ◽  
Risk Process ◽  
Insurance Risk ◽  
Deficit At Ruin ◽  
Scale Functions ◽  
The Deficit At Ruin ◽  
The Laplace Transform ◽  
Surplus Before Ruin ◽  
Set Up ◽  
Spectrally Negative Lévy Processes

AbstractWe consider a Cramér–Lundberg insurance risk process with the added feature of reinsurance. If an arriving claim finds the reserve below a certain threshold γ, or if it would bring the reserve below that level, then a reinsurer pays part of the claim. Using fluctuation theory and the theory of scale functions of spectrally negative Lévy processes, we derive expressions for the Laplace transform of the time to ruin and of the joint distribution of the deficit at ruin and the surplus before ruin. We specify these results in much more detail for the threshold set-up in the case of proportional reinsurance.

scholarly journals Gerber–Shiu distribution at Parisian ruin for Lévy insurance risk processes

2016 ◽  
Vol 53 (2) ◽  
pp. 572-584 ◽  
Author(s):  
Erik J. Baurdoux ◽  
Juan Carlos Pardo ◽  
José Luis Pérez ◽  
Jean-François Renaud
Keyword(s):  
Risk Process ◽  
Levy Processes ◽  
Insurance Company ◽  
Excursion Theory ◽  
Insurance Risk ◽  
Scale Functions ◽  
Surplus Process ◽  
Parisian Ruin ◽  
Risk Processes ◽  
Spectrally Negative Lévy Processes

Abstract Inspired by the works of Landriault et al. (2011), (2014), we study the Gerber–Shiu distribution at Parisian ruin with exponential implementation delays for a spectrally negative Lévy insurance risk process. To be more specific, we study the so-called Gerber–Shiu distribution for a ruin model where at each time the surplus process goes negative, an independent exponential clock is started. If the clock rings before the surplus becomes positive again then the insurance company is ruined. Our methodology uses excursion theory for spectrally negative Lévy processes and relies on the theory of so-called scale functions. In particular, we extend the recent results of Landriault et al. (2011), (2014).

scholarly journals A Lévy Insurance Risk Process with Tax

2008 ◽  
Vol 45 (02) ◽  
pp. 363-375 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Jean-François Renaud ◽  
Xiaowen Zhou
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Risk Process ◽  
Fluctuation Theory ◽  
Insurance Risk ◽  
Exit Problem ◽  
Tax Payments ◽  
Aggregate Income

Using fluctuation theory, we solve the two-sided exit problem and identify the ruin probability for a general spectrally negative Lévy risk process with tax payments of a loss-carry-forward type. We study arbitrary moments of the discounted total amount of tax payments and determine the surplus level to start taxation which maximises the expected discounted aggregate income for the tax authority in this model. The results considerably generalise those for the Cramér-Lundberg risk model with tax.

scholarly journals RUIN PROBABILITIES UNDER AN OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE POLICY IN A JUMP DIFFUSION RISK PROCESS

2009 ◽  
Vol 51 (1) ◽  
pp. 34-48 ◽  
Author(s):  
YIPING QIAN ◽  
XIANG LIN
Keyword(s):  
Ruin Probability ◽  
Market Price ◽  
Optimal Investment ◽  
Jump Diffusion ◽  
Risk Process ◽  
Closed Form Expression ◽  
Proportional Reinsurance ◽  
Insurance Company ◽  
Risky Assets ◽  
Price Of Risk

AbstractIn this paper, we consider an insurance company whose surplus (reserve) is modeled by a jump diffusion risk process. The insurance company can invest part of its surplus in n risky assets and purchase proportional reinsurance for claims. Our main goal is to find an optimal investment and proportional reinsurance policy which minimizes the ruin probability. We apply stochastic control theory to solve this problem. We obtain the closed form expression for the minimal ruin probability, optimal investment and proportional reinsurance policy. We find that the minimal ruin probability satisfies the Lundberg equality. We also investigate the effects of the diffusion volatility parameter, the market price of risk and the correlation coefficient on the minimal ruin probability, optimal investment and proportional reinsurance policy through numerical calculations.

Sign in / Sign up

Export Citation Format

Share Document