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Essays in Stochastic Modeling with Applications to Economics, Finance, and Insurance.
Dissertation Advisor: Stanley Pliska
Description: This dissertation includes three essays. All three essays extensively use the theory of marked point processes. The first essays developed a reduced-form credit risk model of a serial defaulting obligor. The price of a bond with the potential for multiple defaults and rating migration was developed, leveraging the doubly-stochastic marked point process theory. The paper contributes to the literature by providing a comprehensive valuation framework based on the spot hazard rate rather than the forward hazard rate. The second essay determined the optimal capital stock investment under catastrophic risk. The paper extends the simple Solow growth model to include stochastic capital with jumps. The paper solves the Hamilton-Jacobi-Bellman (HJB) for optimal capital investment. The solution suggests that catastrophes reduce the useful life of physical capital, leading to under-investment. The third essay models an individual's consumption, investment, and insurance decisions when the value of financial and insurable assets is subject to the same catastrophic risks. The paper finds that consumption, financial, and insurance decisions are not separable under a joint risk exposure.
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