Super brownian motion conditioning finance

超布朗运动调节金融

• 批准号: 8000-2010
• 负责人: Salisbury, Thomas
• 金额: $ 2.19万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=568550
• 关键词: Super; brownian; motion; conditioning; finance

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.

索尔兹伯里将研究从概率论的三个不同领域所产生的问题。 他的最优控制保证生活福利（GLiB）项目关注的是新一代的退休储蓄产品，包括GLiB的。这些基本上是提供下行保护的选择，并将金融和精算风险联系在一起。现有文献重点关注这些产品从行业角度的风险管理（即定价和对冲）。索尔兹伯里建议从购买者的角度研究他们的最佳控制和管理。例如，确定何时持有其中一些产品是最佳选择，即使存在其他投资，保险或年金产品（并取决于收费水平）。 他的条件超布朗运动的项目是关于推断概率的人口过去的家谱，条件的信息，其未来。因此，这个数学问题类似于进化生物学的几个重要问题。以前的工作大大增加了未来信息的类型，可以纳入，但这样做提出了许多新的和有趣的问题。 他的随机环境中的随机游动（RWRE）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（均匀椭圆率）的标准假设。到目前为止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。该项目有助于理解通过无序介质的传输，这是统计物理学中出现的一个重要课题。