Economics - Research Publications

Permanent URI for this collection

http://hdl.handle.net/11343/417

Filters

2001 - 2002 7
4 3
Reset filters

Settings
Statistics
Citations
Author: Dickson, David × End date: 2002 × Start date: 2000 ×

Search Results

Now showing 1 - 7 of 7
  • Item
    Thumbnail Image
    The Distribution of the time to Ruin in the Classical Risk Model
    Dickson, DCM ; Waters, HR (Cambridge University Press (CUP), 2002-01-01)
    Abstract We study the distribution of the time to ruin in the classical risk model. We consider some methods of calculating this distribution, in particular by using algorithms to calculate finite time ruin probabilities. We also discuss calculation of the moments of this distribution.
  • Item
    Thumbnail Image
    The Gerber-Shiu discounted penalty function in the stationary renewal risk model
    Willmot, Gordon E. ; Dickson, David C. M. ( 2002-08)
    The discounted penalty function introduced by Gerber and Shiu (1998) is considered in the stationary renewal risk model, where it is expressed in terms of the same discounted penalty function in the ordinary renewal risk model. This relationship unifies and generalizes known special cases. An invariance property between the stationary renewal risk model and the classical Poisson model with respect to the ruin probability is also generalized as a result.
  • Item
    Thumbnail Image
    On the expected discounted penalty function at ruin of a surplus process with interest
    Cai, Jun ; Dickson, David C.M. ( 2001-11)
    In this paper, we study the expected value of a discounted penalty function at ruin of the classical surplus process modified by the inclusion of interest of the surplus. The 'penalty' is simply a function of the surplus immediately prior to ruin and the deficit at ruin. An integral equation for the expected value is derived, while the exact solution is given when the initial surplus is zero. Dickson's (1992) formulae for the distribution of the surplus immediately prior to ruin in the classical surplus process are generalised to our modified surplus process.
  • Item
    Thumbnail Image
    Ruin Probabilities with a Markov Chain Interest Model
    Cai, Jun ; Dickson, David C. M. ( 2002-08)
    Ruin probabilities in two generalized discrete time risk processes with a Markov chain interest model are studied. Recursive and integrat equations for the ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived both by inductive and martingale approaches. The relationships between these inequalities are discussed. A numerical example is given to illustrate these results.
  • Item
    Thumbnail Image
    Modern landmarks in actuarial science
    DICKSON, DCM (The Institute of Actuaries of Australia, 2001)
  • Item
    Thumbnail Image
    On the time to ruin for Erlang(2) risk processes
    Dickson, DCM ; Hipp, C (ELSEVIER SCIENCE BV, 2001-12-20)
  • Item
    Thumbnail Image
    A Note on the Maximum Severity of Ruin and Related Problems
    Dickson, David C. M. ( 2002-05)
    Picard (1994) defines the maximum severity of ruin to be the largest deficit of a classical surplus process. Starting from initial surplus Mu, between the time of ruin and the time of recovery to surplus level 0. He gives a simple expression for the distribution function of Mu in terms of the probability of ultimate ruin. This paper first addresses the question of calculating the moments of Mu. It is not easy to achieve explicit expressions for these despite knowing the distribution function of Mu. We consider situations where explicit expressions can be obtained,as well as approximations. We also consider the closely related question of the maximum surplus prior to ruin