“The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model,” Jiandong Ren, July 2007

2008 ◽  
Vol 12 (2) ◽  
pp. 210-212 ◽  
Author(s):  
Andrei L. Badescu
Keyword(s):  
Joint Distribution ◽  
Deficit At Ruin ◽  
Sparre Andersen Model ◽  
Andersen Model ◽  
The Deficit At Ruin

scholarly journals The Joint Density of the Surplus Before and After Ruin in the Sparre Andersen Model

2007 ◽  
Vol 44 (3) ◽  
pp. 695-712 ◽  
Author(s):  
Susan M. Pitts ◽  
Konstadinos Politis
Keyword(s):  
Classical Model ◽  
Joint Density ◽  
Deficit At Ruin ◽  
Sparre Andersen Model ◽  
Andersen Model ◽  
Time Of Ruin ◽  
Collective Risk ◽  
Before And After ◽  
The Deficit At Ruin ◽  
The Time Of Ruin

Gerber and Shiu (1997) have studied the joint density of the time of ruin, the surplus immediately before ruin, and the deficit at ruin in the classical model of collective risk theory. More recently, their results have been generalised for risk models where the interarrival density for claims is nonexponential, but belongs to the Erlang family. Here we obtain generalisations of the Gerber-Shiu (1997) results that are valid in a general Sparre Andersen model, i.e. for any interclaim density. In particular, we obtain a generalisation of the key formula in that paper. Our results are made more concrete for the case where the distribution between claim arrivals is phase-type or the integrated tail distribution associated with the claim size distribution belongs to the class of subexponential distributions. Furthermore, we obtain conditions for finiteness of the joint moments of the surplus before ruin and the deficit at ruin in the Sparre Andersen model.

scholarly journals The Joint Density of the Surplus Before and After Ruin in the Sparre Andersen Model

2007 ◽  
Vol 44 (03) ◽  
pp. 695-712 ◽  
Author(s):  
Susan M. Pitts ◽  
Konstadinos Politis
Keyword(s):  
Classical Model ◽  
Joint Density ◽  
Deficit At Ruin ◽  
Sparre Andersen Model ◽  
Andersen Model ◽  
Time Of Ruin ◽  
Collective Risk ◽  
Before And After ◽  
The Deficit At Ruin ◽  
The Time Of Ruin

Gerber and Shiu (1997) have studied the joint density of the time of ruin, the surplus immediately before ruin, and the deficit at ruin in the classical model of collective risk theory. More recently, their results have been generalised for risk models where the interarrival density for claims is nonexponential, but belongs to the Erlang family. Here we obtain generalisations of the Gerber-Shiu (1997) results that are valid in a general Sparre Andersen model, i.e. for any interclaim density. In particular, we obtain a generalisation of the key formula in that paper. Our results are made more concrete for the case where the distribution between claim arrivals is phase-type or the integrated tail distribution associated with the claim size distribution belongs to the class of subexponential distributions. Furthermore, we obtain conditions for finiteness of the joint moments of the surplus before ruin and the deficit at ruin in the Sparre Andersen model.

scholarly journals Lundberg-type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin under a Markov-modulated Risk Model

2005 ◽  
Vol 35 (02) ◽  
pp. 351-361 ◽  
Author(s):  
Andrew C.Y. Ng ◽  
Hailiang Yang
Keyword(s):  
Regime Switching ◽  
Joint Distribution ◽  
Risk Model ◽  
Insurance Risk ◽  
Additive Process ◽  
Deficit At Ruin ◽  
Markov Additive Process ◽  
The Deficit At Ruin ◽  
Markov Modulated ◽  
Markovian Regime Switching

In this paper, we consider a Markov-modulated risk model (also called Markovian regime switching insurance risk model). Follow Asmussen (2000, 2003), by using the theory of Markov additive process, an exponential martingale is constructed and Lundberg-type upper bounds for the joint distribution of surplus immediately before and at ruin are obtained. As a natural corollary, bounds for the distribution of the deficit at ruin are obtained. We also present some numerical results to illustrate the tightness of the bound obtained in this paper.

Sign in / Sign up

Export Citation Format

Share Document