Huang, Huaxiong2015-12-162015-12-162014-12-172015-12-16http://hdl.handle.net/10315/30645The dissertation focuses on two problems applied to personal financial management for individuals, either before or after retirement. The first topic examines a lifetime ruin probability (LRP) model in which a jump-diffusion process drives the investment return of the agent. The value of the LRP is important to an investor who wants to find out the probability of running out of money, while maintaining a desired standard of living for the rest of his life. Our model leads to a partial-integro-differential equation (PIDE) which is solved by a numerical algorithm. Results are compared against diffusion-related LRP values that do not assume jumps by using calibrated parameters. Retirees are often exposed to large and unpredictable medical expenses due to health shocks. The second topic examines the effect of health shocks and mortality risk on the optimal medical insurance-consumption-allocation strategy. We also derived a solution for the optimal retirement-triggering wealth in a life-cycle framework. As in the first problem, we investigated model changes, for asset return rates which obey a jump-diffusion dynamics.enAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.MathematicsFinanceElectronic Thesis or Dissertation2015-12-16Lifetime Ruin ProbabilityJump Diffusion ProcessesOptimal Control ProblemCritical Retirement Triggering Wealth