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  • Ruin Problems with Risky Investments

    Creator:
    Loke, Sooie-Hoe
    Abstract:
    In this dissertation, we study two risk models. First, we consider the dual risk process which models the surplus of a company that incurs expenses at a constant rate and earns random positive gains at random times. When the surplus is invested in a risky asset following a geometric Brownian...
    Resource Type:
    Dissertation
    Full Text:
    geometric Brownian motion, we derive a parabolic integro-partial-differential equation (IPDE) for the

  • Skew Brownian motion and branching processes applied to diffusion-advection in heterogenous media and fluid flow

    Creator:
    Ramirez, Jorge M.
    Abstract:
    This thesis contains three manuscripts addressing the application of stochastic processes to the analysis and solution of partial differential equations (PDEs) in mathematical physics. In the first manuscript, one dimensional diffusion and Burgers equation are considered. The Fourier transform of the solution to each PDE is represented as the expected...
    Resource Type:
    Dissertation
    Full Text:
    physics. In the first manuscript, one dimensional diffusion and Burgers equation are considered. The