Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

Excessive functions, Appell polynomials and optimal stopping

The main topic of the thesis is optimal stopping. This is treated in two research articles. In the first article we introduce a new approach to optimal stopping of general strong Markov processes. The approach is based on the representation of excessive functions as expected suprema. We present a variety of examples, in particular, the Novikov-Shiryaev problem for Lévy processes. In the second article on optimal stopping we focus on differentiability of excessive functions of diffusions and apply these results to study the validity of the principle of smooth fit. As an example we discuss optimal stopping of sticky Brownian motion. The third research article offers a survey like discussion on Appell polynomials. The crucial role of Appell polynomials in optimal stopping of Lévy processes was noticed by Novikov and Shiryaev. They described the optimal rule in a large class of problems via these polynomials. We exploit the probabilistic approach to Appell polynomials and show that many classical results are obtained with ease in this framework. In the fourth article we derive a new relationship between the generalized Bernoulli polynomials and the generalized Euler polynomials.

An optimal sequential procedure for a buying-selling problem with independent observations

We consider a buying-selling problem when two stops of a sequence of independent random variables are required. An optimal stopping rule and the value of a game are obtained.

Optimal eradication: when to stop looking for an invasive plant

The notion of being sure that you have completely eradicated an invasive species is fanciful because of imperfect detection and persistent seed banks. Eradication is commonly declared either on an ad hoc basis, on notions of seed bank longevity, or on setting arbitrary thresholds of 1% or 5% confidence that the species is not present. Rather than declaring eradication at some arbitrary level of confidence, we take an economic approach in which we stop looking when the expected costs outweigh the expected benefits. We develop theory that determines the number of years of absent surveys required to minimize the net expected cost. Given detection of a species is imperfect, the optimal stopping time is a trade-off between the cost of continued surveying and the cost of escape and damage if eradication is declared too soon. A simple rule of thumb compares well to the exact optimal solution using stochastic dynamic programming. Application of the approach to the eradication programme of Helenium amarum reveals that the actual stopping time was a precautionary one given the ranges for each parameter.

Valuing American Derivatives by Least Squares Methods

Least Squares estimators are notoriously known to generate sub-optimal exercise decisions when determining the optimal stopping time. The consequence is that the price of the option is underestimated. We show how variance reduction methods can be implemented to obtain more accurate option prices. We also extend the Longsta¤ and Schwartz (2001) method to price American options under stochastic volatility. These are two important contributions that are particularly relevant for practitioners. Finally, we extend the Glasserman and Yu (2004b) methodology to price Asian options and basket options.

Life-Cycle, Effort and Academic Inactivity

It has been observed that university professors sometimes become less research active in their later years. This paper models the decision to become inactive as a utility maximising problem under conditions of uncertainty and derives an age-dependent activity condition for the level of research productivity. The model implies that professors who are close to retirement age are more likely to become inactive when faced with setbacks in their research while those who continue research do not lower their activity levels. Using data from the University of Iceland, we find support for the model’s predictions. The model suggests that universities should induce their older faculty to remain research active by striving to make their research more productive and enjoyable, maintaining peer pressure, reducing job security and offering higher performance related pay.

When to Quit Under Uncertainty? A real options approach to smoking cessation

This paper models the decision to quit smoking like an investment decision where the quitter incurs a sunk withdrawal cost today and forgoes their consumer surplus from cigarettes (invests) and hopes to reap an uncertain reward of better health and therefore higher utility in the future (return). We show that a risk-averse mature smoker who expects to benefit from quitting may still rationally choose to delay quitting until they are more confident that quitting is the right decision for them. Such a decision by the smoker is due to the value associated with keeping their option of whether or not to quit open as they learn more about the damage that smoking will have on their future utility. Policies which reduce a smoker’s uncertainty about the damage that smoking with have on their future utility is likely to make them quit earlier.

Ensaios em Finanças

Esta tese é composta de três artigos sobre finanças. O primeiro tem o título "Nonparametric Option Pricing with Generalized Entropic Estimators " e estuda um método de apreçamento de derivativos em mercados incompletos. Este método está relacionado com membros da família de funções de Cressie-Read em que cada membro fornece uma medida neutra ao risco. Vários testes são feitos. Os resultados destes testes sugerem um modo de definir um intervalo robusto para preços de opções. Os outros dois artigos são sobre anúncios agendados em diferentes situações. O segundo se chama "Watching the News: Optimal Stopping Time and Scheduled Announcements" e estuda problemas de tempo de parada ótimo na presença de saltos numa data fixa em modelos de difusão com salto. Fornece resultados sobre a otimalidade do tempo de parada um pouco antes do anúncio. O artigo aplica os resultados ao tempo de exercício de Opções Americanas e ao tempo ótimo de venda de um ativo. Finalmente o terceiro artigo estuda um problema de carteira ótima na presença de custo fixo quando os preços podem saltar numa data fixa. Seu título é "Dynamic Portfolio Selection with Transactions Costs and Scheduled Announcement" e o resultado mais interessante é que o comportamento do investidor é consistente com estudos empíricos sobre volume de transações em momentos próximos de anúncios.

Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing

Thesis (Ph.D.)--University of Washington, 2016-08

Essays in environmental economic valuation and decision making in the presence of an environmental disaster

The first essay developed a respondent model of Bayesian updating for a double-bound dichotomous choice (DB-DC) contingent valuation methodology. I demonstrated by way of data simulations that current DB-DC identifications of true willingness-to-pay (WTP) may often fail given this respondent Bayesian updating context. Further simulations demonstrated that a simple extension of current DB-DC identifications derived explicitly from the Bayesian updating behavioral model can correct for much of the WTP bias. Additional results provided caution to viewing respondents as acting strategically toward the second bid. Finally, an empirical application confirmed the simulation outcomes. The second essay applied a hedonic property value model to a unique water quality (WQ) dataset for a year-round, urban, and coastal housing market in South Florida, and found evidence that various WQ measures affect waterfront housing prices in this setting. However, the results indicated that this relationship is not consistent across any of the six particular WQ variables used, and is furthermore dependent upon the specific descriptive statistic employed to represent the WQ measure in the empirical analysis. These results continue to underscore the need to better understand both the WQ measure and its statistical form homebuyers use in making their purchase decision. The third essay addressed a limitation to existing hurricane evacuation modeling aspects by developing a dynamic model of hurricane evacuation behavior. A household's evacuation decision was framed as an optimal stopping problem where every potential evacuation time period prior to the actual hurricane landfall, the household's optimal choice is to either evacuate, or to wait one more time period for a revised hurricane forecast. A hypothetical two-period model of evacuation and a realistic multi-period model of evacuation that incorporates actual forecast and evacuation cost data for my designated Gulf of Mexico region were developed for the dynamic analysis. Results from the multi-period model were calibrated with existing evacuation timing data from a number of hurricanes. Given the calibrated dynamic framework, a number of policy questions that plausibly affect the timing of household evacuations were analyzed, and a deeper understanding of existing empirical outcomes in regard to the timing of the evacuation decision was achieved.

Essays in Environmental Economic Valuation and Decision Making in the Presence of an Environmental Disaster

The first essay developed a respondent model of Bayesian updating for a double-bound dichotomous choice (DB-DC) contingent valuation methodology. I demonstrated by way of data simulations that current DB-DC identifications of true willingness-to-pay (WTP) may often fail given this respondent Bayesian updating context. Further simulations demonstrated that a simple extension of current DB-DC identifications derived explicitly from the Bayesian updating behavioral model can correct for much of the WTP bias. Additional results provided caution to viewing respondents as acting strategically toward the second bid. Finally, an empirical application confirmed the simulation outcomes. The second essay applied a hedonic property value model to a unique water quality (WQ) dataset for a year-round, urban, and coastal housing market in South Florida, and found evidence that various WQ measures affect waterfront housing prices in this setting. However, the results indicated that this relationship is not consistent across any of the six particular WQ variables used, and is furthermore dependent upon the specific descriptive statistic employed to represent the WQ measure in the empirical analysis. These results continue to underscore the need to better understand both the WQ measure and its statistical form homebuyers use in making their purchase decision. The third essay addressed a limitation to existing hurricane evacuation modeling aspects by developing a dynamic model of hurricane evacuation behavior. A household’s evacuation decision was framed as an optimal stopping problem where every potential evacuation time period prior to the actual hurricane landfall, the household’s optimal choice is to either evacuate, or to wait one more time period for a revised hurricane forecast. A hypothetical two-period model of evacuation and a realistic multi-period model of evacuation that incorporates actual forecast and evacuation cost data for my designated Gulf of Mexico region were developed for the dynamic analysis. Results from the multi-period model were calibrated with existing evacuation timing data from a number of hurricanes. Given the calibrated dynamic framework, a number of policy questions that plausibly affect the timing of household evacuations were analyzed, and a deeper understanding of existing empirical outcomes in regard to the timing of the evacuation decision was achieved.