<p> The goal of this thesis is to study the economics of computational learning. Attention is also paid to applications of computational learning models, especially Valiant's so-called `probably approximately correctly' (PAC) learning model, in econometric situations.</p><p>Specifically, an economically reasonable stopping time model of learning is the subject of two attached papers. In the rst paper, Paper A, the economics of PAC learning are considered. It is shown how a general form of the optimal stopping time bounds can be achieved using the PAC convergence rates for a `pessimistic-rational' learner in the most standard binary case of passive supervised PAC model of finite Vapnik-Chervonenkis (VC) dimension.</p><p> </p><p>The second paper, Paper B, states precisely and improves the ideas introduced in Paper A and tests them in a specific and mathematically simple case. Using the maxmin procedure of Gilboa and Schmeidler the bounds for the stopping time are expressed in terms of the largest expected error of recall, and thus, effectively, in terms of the least expected reward. The problem of locating a real number θ by testing whether x_i ≤ θ , with x_i drawn from an calculated for a range of term rates, sample costs and rewards/penalties from a recall ae included. The standard econometric situations, such as product promotion, market research, credit risk assessment, and bargaining and tenders, where such bounds could be of interest, are pointed. </p><p>These two papers are the essence of this thesis, and form it togheter with an introduction to the subject of learning.</p> / <p>Målet med denna avhandling är att studera optimering av inlärning när det finns kostnader. Speciellt studerar jag Valiants så kallade PAC-inlärningsmodell  (Probably Approximately Correctly), ofta använd inom datavetenskap. I två artiklar behandlar jag hur länge, ur ekonomisk synvinkel, inlärningsperioden bör fortsätta.</p><p>I den första artikeln visar vi hur en generell form av begränsningar av den optimala inlärningsperioden kan fås med hjälp av PAC-konvergenshastigheten för en ’pessimistiskt rationell’ studerande (i det vanligaste binära fallet av passiv PAC-inlärningsmodell med ändlig VC-dimension).</p><p>I den andra artikeln fördjupar och förbättrar vi idéerna från den första artikeln, och testar dem i en specifik situation som är matematiskt enkel. Med hjälp av Gilboa – Schmeidlers max - minprocedur  uttrycker vi begränsningarna av den optimala inlärningsperioden som funktion av det största förväntade felet och därmed som funktion av den minsta förväntade belöningen. Vi diskuterar problemet med att hitta ett reellt tal θ genom testning av huruvida x_i ≤ θ, där x_i dras från en okänd fördelning. Här tar vi också upp exempel på begränsningar av inlärningsperioden, beräknade för en mängd av diskontovärden, stickprovskostnader och belöning/straff för erinran, samt en del vanliga ekonometriska situationer där sådana begränsningar är av intresse, såsom marknadsföring av produkter, marknadsanalys, kreditriskskattning och offertförhandling.</p><p>Avhandlingen består i huvuddel av dessa två artiklar samt en kort introduktion till ekonomiska, matematiska och datavetenskapliga inlärningsmodeller.</p><p> </p>

Degree: Master of Science Department: Science / The superharmonic characterization of the value function is proved, under the assumption that an optimal stopping time exists. The fair price of an American contingent claim is established as an optimal stopping problem. The price of the perpetual Russian option is derived, using the dual martingale measure to reduce the dimension of the problem. American barrier options are discussed, and the solution to the perpetual American up-and-out put is derived. The price of the American put on a finite time horizon is shown to be the price of the European put plus an early exercise premium, through the use of a local time-space formula. The optimal stopping boundary is characterised as the unique increasing solution of a non-linear integral equation. Finally, the integral representation of the price of an American floating strike Asian call with arithmetic averaging is derived.

The goal of this thesis is to study the economics of computational learning. Attention is also paid to applications of computational learning models, especially Valiant's so-called `probably approximately correctly' (PAC) learning model, in econometric situations. Specifically, an economically reasonable stopping time model of learning is the subject of two attached papers. In the rst paper, Paper A, the economics of PAC learning are considered. It is shown how a general form of the optimal stopping time bounds can be achieved using the PAC convergence rates for a `pessimistic-rational' learner in the most standard binary case of passive supervised PAC model of finite Vapnik-Chervonenkis (VC) dimension.   The second paper, Paper B, states precisely and improves the ideas introduced in Paper A and tests them in a specific and mathematically simple case. Using the maxmin procedure of Gilboa and Schmeidler the bounds for the stopping time are expressed in terms of the largest expected error of recall, and thus, effectively, in terms of the least expected reward. The problem of locating a real number θ by testing whether xi ≤ θ , with xi drawn from an calculated for a range of term rates, sample costs and rewards/penalties from a recall ae included. The standard econometric situations, such as product promotion, market research, credit risk assessment, and bargaining and tenders, where such bounds could be of interest, are pointed.  These two papers are the essence of this thesis, and form it togheter with an introduction to the subject of learning. / Målet med denna avhandling är att studera optimering av inlärning när det finns kostnader. Speciellt studerar jag Valiants så kallade PAC-inlärningsmodell  (Probably Approximately Correctly), ofta använd inom datavetenskap. I två artiklar behandlar jag hur länge, ur ekonomisk synvinkel, inlärningsperioden bör fortsätta. I den första artikeln visar vi hur en generell form av begränsningar av den optimala inlärningsperioden kan fås med hjälp av PAC-konvergenshastigheten för en ’pessimistiskt rationell’ studerande (i det vanligaste binära fallet av passiv PAC-inlärningsmodell med ändlig VC-dimension). I den andra artikeln fördjupar och förbättrar vi idéerna från den första artikeln, och testar dem i en specifik situation som är matematiskt enkel. Med hjälp av Gilboa – Schmeidlers max - minprocedur  uttrycker vi begränsningarna av den optimala inlärningsperioden som funktion av det största förväntade felet och därmed som funktion av den minsta förväntade belöningen. Vi diskuterar problemet med att hitta ett reellt tal θ genom testning av huruvida xi ≤ θ, där xi dras från en okänd fördelning. Här tar vi också upp exempel på begränsningar av inlärningsperioden, beräknade för en mängd av diskontovärden, stickprovskostnader och belöning/straff för erinran, samt en del vanliga ekonometriska situationer där sådana begränsningar är av intresse, såsom marknadsföring av produkter, marknadsanalys, kreditriskskattning och offertförhandling. Avhandlingen består i huvuddel av dessa två artiklar samt en kort introduktion till ekonomiska, matematiska och datavetenskapliga inlärningsmodeller.

In prophet problems, two players with different levels of information make decisions to optimize their return from an underlying optimal stopping problem. The player with more information is called the "prophet" while the player with less information is known as the "gambler." In this thesis, as in the majority of the literature on such problems, we assume that the prophet is omniscient, and the gambler does not know future outcomes when making his decisions. Certainly, the prophet will get a better return than the gambler. But how much better? The goal of a prophet problem is to find the least upper bound on the difference (or ratio) between the prophet's return, M, and the gambler's return, V. In this thesis, we present new prophet problems where we seek the least upper bound on M-V when there is a fixed cost per observations. Most prophet problems in the literature compare M and V when prophet and gambler buy (or sell) one asset. The new prophet problems presented in Chapters 3 and 4 treat a scenario where prophet and gambler optimize their return from selling two assets, when there is a fixed cost per observation. Sharp bounds for the problems on small time horizons are given; for the n-day problem, rough bounds and a description of the distributions for the random variables that maximize M-V are presented.

This thesis consists of an introduction and five articles. A common theme in all the articles is optimal timing when acting on a financial market. The main topics are optimal selling of an asset, optimal exercising of an American option, optimal stopping games and optimal strategies in trend following trading. In all the articles, we consider a financial market different from the standard Black-Scholes market. In two of the articles this difference consists in allowing for jumps of the underlying process. In the other three, the difference is that we have incomplete information about the drift of the underlying process. This is a natural assumption in many situations, including the case of a true buyer of an American option, trading in a market which exhibits trends, and optimal liquidation of an asset in the presence of a bubble. These examples are all addressed in this thesis.

This thesis utilizes the binary encounter approximation to calculate the stopping power of protons penetrating silicon. The main goal of the research was to make predictions of the stopping power of silicon for low-energy and medium-energy channelled protons, in the hope that this will motivate experiments to test the theory developed below. In attaining this goal, different stopping power theories were compared and the binary encounter approach was applied to random (non-channelled) and high-energy channelled protons in silicon, and these results were compared with experimental data.

ABSTRACT A continuous energy loss measurements of 63Cu, 28Si, 27AI, 24Mg, 19F, 160 and 12C ions over an energy range of(O.OG-0.65) MeV/nucleon through thin polymeric foils (Mylar, Polypropylene and Formvar) were carried out by time of flight spectrometry. The deduced experimental stopping data have been used in order to assess our proposed semi empirical formula. The proposed approach based on the Firsov and Lindhard-Scharff stopping power models is provided for well describing-the electronic stopping power of heavy ions (3 Z < 100) in various solids targets at low energy range. The '· factor, which was approximated to be z:i6 , involved in Lindhard, Scharff and Schiott (LSS) formula has been suitably modified in the light of the available experimental stopping power data. The calculated stopping power values after incorporating, effective charge z; of moving heavy ions with low velocities ( v v0z 13 ) and modified C. in LSS formula, have been found to be in close agreement with measured values in various solids targets. A reason of energy loss measurements is to obtain data that help to assess our understanding of the stopping power theories. For this, the obtained results are compared with, LSS calculations, MSTAR and SRIM-2013 predictions code.

No description available.

Ubiquitous computing results in access to vast amounts of data, which is changing the way humans interact with each other, with computers, and with their environments. Information is literally at our fingertips with touchscreen technology, but it is not valuable until it is understood. As a result, selecting which information to use in a decision process is a challenge in the current information environment (Lu & Yuan, 2011). The purpose of this dissertation was to investigate how individual decision makers, in different decision contexts, determine when to stop collecting information given the availability of virtually unlimited information. Decision makers must make an ultimate decision, but also must make a decision that he or she has enough information to make the final decision (Browne, Pitts, & Wetherbe, 2007). In determining how much information to collect, researchers found that people engage in ‘satisficing' in order to make decisions, particularly when there is more information than it is possible to manage (Simon, 1957). A more recent elucidation of information use relies on the idea of stopping rules, identifying five common stopping rules information seekers use: mental list, representational stability, difference threshold, magnitude threshold, and single criterion (Browne et al., 2007). Prior research indicates a lack of understanding in the areas of information use (Prabha, Connaway, Olszewski, & Jenkins, 2007) and information overload (Eppler & Mengis, 2004) in Information Systems literature. Moreover, research indicates a lack of clarity in what information should be used in different decision contexts (Kowalczyk & Buxmann, 2014). The increase in the availability of information further complicates and necessitates research in this area. This dissertation seeks to fill these gaps in the literature by determining how information use changes across decision contexts and the relationships between stopping rules. Two unique methodologies were used to test the hypotheses in the conceptual model, which both contribute to research on information stopping rules. One tracks the participant during an online search, the second asks follow-up survey questions on a Likert scale. One of four search tasks (professional or personal context and a big data analytics understanding or restaurant location search) was randomly assigned to each participant. Results show different stopping rules are more useful for different decision contexts. Specifically, professional tasks are more likely to use stopping rules with an a priori decision on how much information to collect, while personal tasks encourage users to determine how much information to collect during the search process. The analysis also shows that different stopping rules have different emphases on quality and quantity of information. Specifically, representational stability requires both a high quality and quantity of information, while other stopping rules indicate a preference for one of the two. Finally, information quality and quantity ultimately have a positive relationship with decision confidence, satisfaction, and efficiency. The findings of this research are useful to practitioners and academics tackling issues with the availability of more information. As systems are designed for information search, understanding information stopping rules become increasingly important.

Test-analyze-and-fix (TAAF) is the most commonly recognized method of improving system reliability. The work presented here addresses the question of when to stop testing during TAAF programs involving one-shot systems when the number of systems to be produced is predetermined and the probabilities of identifying and successfully correcting each failure mode are less than one. The goal here is to determine when to cease testing to maximize utility where utility is defined as the number of systems expected to perform successfully in the field after deployment of the lot. Two TAAF stopping rules are presented. Simulation is used to model TAAF execution under different reliability growth conditions. Four discrete reliability growth models (DRGM's) are used to generate "real world" reliability growth and to estimate reliability growth using hypothetical observed success/failure data. Ranges for the following parameters are considered: starting reliability, growth rate, maximum achievable reliability, number of systems to be produced, probability of incorrectly identifying a failure mode, and probability of an unsuccessful design modification. Conclusions are drawn regarding stopping rule performance in terms of stopping rule signal location, utility loss, achieved reliability, and fraction tested. Both rules perform well and are implementable from a practical standpoint. Specific recommendations for stopping rule implementation are given based on the controllable factors, estimation methodology and lot size. / Master of Science