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dc.contributor.authorRen, Danen_US
dc.date.accessioned2015-09-24T15:47:59Z
dc.date.available2015-09-24T15:47:59Z
dc.date.issued2013
dc.identifier.urihttps://hdl.handle.net/2144/13130
dc.description.abstractMy PhD thesis concentrates on the field of stochastic analysis, with focus on stochastic optimization and applications in finance. It is composed of two parts: the first part studies an optimal stopping problem, and the second part studies an optimal control problem. The first topic considers a one-dimensional transient and downwards drifting diffusion process X, and detects the optimal times of a random time(denoted as ρ). In particular, we consider two classes of random times: (1) the last time when the process exits a certain level l; (2) the time when the process reaches its maximum. For each random time, we solve the optimization problem infτ E[λ(τ- ρ)+ +(1-λ)(ρ - τ)+] overall all stopping times. For the last exit time, the process should stop optimally when it runs below some fixed level k the first time, where k is the solution of an explicit defined equation. For the ultimate maximum time, the process should stop optimally when it runs below a boundary which is the maximal positive solution (if exists) of a first-order ordinary differential equation which lies below the line λs for all s > 0 . The second topic solves an optimal consumption and investment problem for a risk-averse investor who is sensitive to declines than to increases of standard living (i.e., the investor is loss averse), and the investment opportunities are constant. We use the tools of stochastic control and duality methods to solve the resulting free-boundary problem in an infinite time horizon. Briefly, the investor consumes constantly when holding a moderate amount of wealth. In bliss time, the investor increases the consumption so that the consumption-wealth ratio reaches some fixed minimum level; in gloom time, the investor decreases the consumption gradually. Moreover, high loss aversion tends to raise the consumption-wealth ratio, but cut the investment-wealth ratio overall.en_US
dc.language.isoen_US
dc.subjectMathematicsen_US
dc.subjectFinancial mathematicsen_US
dc.subjectOptimal consumptionen_US
dc.subjectOptimal controlen_US
dc.subjectOptimal stoppingen_US
dc.subjectStochastic optimizationen_US
dc.titleStochastic optimization and applications in financeen_US
dc.typeThesis/Dissertationen_US
dc.date.updated2015-09-23T20:10:38Z
etd.degree.nameDoctor of Philosophyen_US
etd.degree.leveldoctoralen_US
etd.degree.disciplineMathematics & Statisticsen_US
etd.degree.grantorBoston Universityen_US


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