Dalhousie University Mathematics Colloquium, 2013/14Mathematics Colloquiums are on Mondays, 3:30pm in room 319 in the Chase Building, unless otherwise indicated. There is an alternate time on Thursdays, 2:30pm.
Abstract: Wave phenomena occur on an enormous range of scales, from the sub-quantum mechanical to the astrophysical. This talk will discuss some of the common scale independent features of wave propagation and wave interaction, including detailed descriptions of nonlinear wave collisions and a proposal of a kinetic theory for a regime of wave turbulence.
This talk is jointly organized by Oceanography and Mathematics, and co-sponsored by AARMS.
Hui Zhao (Dalhousie, Rowe School of Business and Tianjin University): "Optimal excess-of-loss reinsurance and investment problem for an insurer with jump-diffusion risk process under the Heston model"
Abstract: In this paper, we study the optimal excess-of-loss reinsurance and investment problem for an insurer with jump-diffusion risk model. The insurer is allowed to purchase reinsurance and invest in one risk-free asset and one risky asset whose price process satisfies the Heston model. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. By applying stochastic optimal control approach, we obtain the optimal strategy and value function explicitly. In addition, a verification theorem is provided and the properties of the optimal strategy are discussed. Finally, we present a numerical example to illustrate the effects of model parameters on the optimal investment-reinsurance strategy and the optimal value function. The talk will be accessible to a general audience.
Abstract: We present three examples of delayed bifurcations for spike solutions of reaction-diffusion systems. The delay effect results as the system passes slowly from a stable to an unstable regime, and was previously analysed in the context of ODE's in [P. Mandel, T. Erneux, J. Stat. Phys, 1987]. It was found that the instability would not be fully realized until the system had entered well into the unstable regime. The bifurcation is said to have been "delayed" relative to the threshold value computed directly from a linear stability analysis. We show that the phenomenon of delay is present also in PDE systems while highlighting some novel features not observed for ODE's. Analytic predictions for the magnitude of the delays are obtained through analysis of certain explicitly solvable nonlocal eigenvalue problems. The theory is confirmed by numerical solutions of the full PDE systems.
For updates and corrections, contact Peter Selinger.