Human beings are living longer than in the past. Their life expectancy has been improved significantly since last century. The demise of Defined Benefit Pensions forces more retirees to use defined contribution pension plan to hedge the longevity risk. So it's possible for the retirees to run out of wealth before run out of life while their current standard of living is maintained. Hence to provide retirement advice, life ruin probability becomes very important.

The stochastic hazard rate is studied when we compute life time ruin probability. This is reasonable since the hazard rate is not a constant, it has ups and downs. The problem is modeled using stochastic differential equations, which is solved by converting the probability into Partial Differential Equations (PDEs). Analytical solutions can not be found to these highly nonlinear equations and numerical methods are the only way to get the approximate ones. Alternative Direction Implicit (ADI) method and Upwind Scheme are chosen to solve the 2D ruin problem. These have significantly reduced the computing time and saved lots of space.

The ruin probability under stochastic hazard rate and deterministic hazard rate is compared. When the stochastic hazard rate collapses to Gompertz Distribution, these two probabilities match very well. The effect of the correlation between wealth and hazard rate is studied. Our results show that when the correlation is positive, the ruin probability is higher, which is consistent to the commonsense.