Super brownian motion conditioning finance

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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.