Abstract
Since the introduction of Two sided movements of risk reserves in the renewal risk theory scenario, the concept has been the major area of analysis for many researchers. Under some elementary assumptions, on approximating appropriate distributions to inter time claim occurrence, the explicit expressions for ruin theory components in the literature could be generated. In this work, we examine probability density of the time of ruin, surplus immediately before ruin and deficit at ruin respectively under two sided risk process using some fundamental assumptions. Explicit expressions for distribution of interest are also being derived.
Reference26 articles.
1. Albretcher, H., Gerber, H.U. and Yang, H. (2010). A Direct Approach to the Discounted Penalty Functions. North American Actuarial Journal, 14, 420-447. https://doi.org/10.1080/10920277.2010.10597599
2. Anderson, E.S. (1957). On the Collective Theory of Risk in Case of Contagion between the Claims. Transactions on XVth International Congress of Actuaries, 2, 219-229.
3. Cai, J. & Yang, H. (2005). Ruin in the Perturbed Compound Poisson Risk Process under Interest Force. Advances in Applied Probability, 37, 819-835. https://doi.org/10.1017/S0001867800000495
4. Chang, V. and Tang, Q (2003). Moments of the Surplus before Ruin and the Deficit at Ruin in the Erlang (2) Risk Process. North American Actuarial Journal, 7, 1-12. https://doi.org/10.1080/10920277.2003.10596073
5. Dickson, D.C.M. & Hipp, C. (2001). On the Time to Ruin for Erlang