Super brownian motion conditioning finance

索尔兹伯里将研究概率论的三个不同领域产生的问题。 他的保证生活福利最优控制(GLib)项目涉及新一代退休储蓄产品，其中包括Glib。这些产品本质上是提供下行保护的选项，它们将金融风险和精算风险联系在一起。现有文献主要从行业层面(即定价和套期保值)对这些产品的风险管理进行研究。索尔兹伯里建议从购买者的角度研究他们的最优控制和管理。例如，确定何时持有其中一些产品是最佳的，即使存在其他投资、保险或年金产品(并取决于收取的费用水平)。 他关于条件超布朗运动的项目是关于推断一个群体过去谱系的概率，条件是关于该群体未来的信息。因此，这个数学问题类似于进化生物学的几个重要问题。以前的工作极大地增加了可以纳入的未来信息的类型，但这样做会带来许多新的和有趣的问题。 他关于随机环境中的随机游动(RWRE)的项目涉及一类新的模型，介于经典RWRE和渗流之间，并且没有关于RWRE(均匀椭圆性)的标准假设。到目前为止所获得的结果包括获得新的方向类型的相变，但渐近速度和方差估计仍然完全开放。这个项目有助于理解无序介质中的输运，这是统计物理学中出现的一个重要课题。

Salisbury will study questions arising from three distinct areas of probability theory. His project on optimal control of guaranteed living benefits (GLiB) project concerns a new generation of retirement savings products incorporate GLiB's. These are essentially options that provide downside protection, and which tie together financial and actuarial risks. The existing literature focuses on risk management of these products from the industry side (ie pricing and hedging). Salisbury proposes to study their optimal control and management, from the purchaser's perspective. For example, determining when it is optimal to hold some of these products, even in the presence of other investment, insurance, or annuity products (and depending on the level of fees charged). His project on conditioned super Brownian motion is about inferring probabilities for the past genealogy of a population, conditioned on information about its future. As such, this mathematical problem is analogous to several important problems of evolutionary biology. Previous work greatly increased the types of future information that can be incorporated, but doing so raised many new and interesting problems. His project on random walks in random environments (RWRE) concerns a new class of models, lying between classical RWRE and percolation, and free of the standard assumptions on RWREs (uniform ellipticity). Results obtained so far include obtaining new directional types of phase transitions, but asymptotic speed and variance estimates remain completely open. This project contributes to the understanding of transport through disordered media, an important topic arising in statistical physics.