dc.contributor.author Ren, Dan en_US dc.date.accessioned 2015-09-24T15:47:59Z dc.date.available 2015-09-24T15:47:59Z dc.date.issued 2013 dc.identifier.uri https://hdl.handle.net/2144/13130 dc.description.abstract My 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. en_US 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. dc.language.iso en_US dc.subject Mathematics en_US dc.subject Financial mathematics en_US dc.subject Optimal consumption en_US dc.subject Optimal control en_US dc.subject Optimal stopping en_US dc.subject Stochastic optimization en_US dc.title Stochastic optimization and applications in finance en_US dc.type Thesis/Dissertation en_US dc.date.updated 2015-09-23T20:10:38Z etd.degree.name Doctor of Philosophy en_US etd.degree.level doctoral en_US etd.degree.discipline Mathematics & Statistics en_US etd.degree.grantor Boston University en_US
﻿