“Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang(2) Risk Process,” Yebin Cheng and Qihe Tang, January 2003

2003 ◽  
Vol 7 (3) ◽  
pp. 122-124 ◽  
Author(s):  
X. Sheldon Lin
Keyword(s):  
Risk Process ◽  
Deficit At Ruin ◽  
The Deficit At Ruin ◽  
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.

The surplus prior to ruin and the deficit at ruin for a correlated risk process

2005 ◽  
Vol 2005 (6) ◽  
pp. 433-445 ◽  
Author(s):  
Andrei L. Badescu ◽  
Lothar Breuer ◽  
Steve Drekic ◽  
Guy Latouche ◽  
David A. Stanford
Keyword(s):  
Risk Process ◽  
Deficit At Ruin ◽  
The Deficit At Ruin

Distributional Study of De Finetti's Dividend Problem for a General Lévy Insurance Risk Process

2007 ◽  
Vol 44 (02) ◽  
pp. 428-443 ◽  
Author(s):  
A. E. Kyprianou ◽  
Z. Palmowski
Keyword(s):  
Net Present Value ◽  
Risk Process ◽  
Excursion Theory ◽  
Insurance Risk ◽  
Present Value ◽  
Deficit At Ruin ◽  
Spectrally Negative Lévy Process ◽  
The Deficit At Ruin ◽  
The Laplace Transform ◽  
Classical Control

We provide a distributional study of the solution to the classical control problem due to De Finetti (1957), Gerber (1969), Azcue and Muler (2005), and Avram et al. (2007), which concerns the optimal payment of dividends from an insurance risk process prior to ruin. Specifically, we build on recent work in the actuarial literature concerning calculations of the nth moment of the net present value of dividends paid out in the optimal strategy as well as the moments of the deficit at ruin and the Laplace transform of the red period. The calculations we present go much further than the existing literature, in that our calculations are valid for a general spectrally negative Lévy process as opposed to the classical Cramér–Lundberg process with exponentially distributed jumps. Moreover, the technique we use appeals principally to excursion theory rather than integro-differential equations and, for the case of the nth moment of the net present value of dividends, makes a new link with the distribution of integrated exponential subordinators.

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