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Full-Text Articles in Numerical Analysis and Computation
Options Pricing And Hedging In A Regime-Switching Volatility Model, Melissa A. Mielkie
Options Pricing And Hedging In A Regime-Switching Volatility Model, Melissa A. Mielkie
Electronic Thesis and Dissertation Repository
Both deterministic and stochastic volatility models have been used to price and hedge options. Observation of real market data suggests that volatility, while stochastic, is well modelled as alternating between two states. Under this two-state regime-switching framework, we derive coupled pricing partial differential equations (PDEs) with the inclusion of a state-dependent market price of volatility risk (MPVR) term.
Since there is no closed-form solution for this pricing problem, we apply and compare two approaches to solving the coupled PDEs, assuming constant Poisson intensities. First we solve the problem using numerical solution techniques, through the application of the Crank-Nicolson numerical scheme. …
Study Of Virus Dynamics By Mathematical Models, Xiulan Lai
Study Of Virus Dynamics By Mathematical Models, Xiulan Lai
Electronic Thesis and Dissertation Repository
This thesis studies virus dynamics within host by mathematical models, and topics discussed include viral release strategies, viral spreading mechanism, and interaction of virus with the immune system.
Firstly, we propose a delay differential equation model with distributed delay to investigate the evolutionary competition between budding and lytic viral release strategies. We find that when antibody is not established, the dynamics of competition depends on the respective basic reproduction numbers of the two viruses. If the basic reproductive ratio of budding virus is greater than that of lytic virus and one, budding virus can survive. When antibody is established for …