29 research outputs found
Simpler proofs in finance and shout options
No full textIn the discrete binomial model for option pricing, the price of an American option is obtained using a backward recursion algorithm. However, the currently available justification for this algorithm is long and circuitous. Similarly, the key result used in the justification for antithetic sampling is not proved in standard financial texts. The proof is relegated to an older article, where the required result is masked by general details about association of random variables. This article gives self-contained, considerably simpler, proofs for both these basic results and extends these results to more general applications. In particular, it settles the question of optimality of early shouting for the buyer of Shout call options.
Bending and compressive strength of lattice structures manufactured by SLM
No full textLAUREA MAGISTRALEQuesto lavoro di tesi tratta principalmente di strutture reticolari f2-BCC e f2-FCC-L, ottenute tramite l’utilizzo di additive manufacturing della lega AlSi10Mg utilizzando la tecnica del Selective Laser Melting (SLM). Queste due tipologie di strutture micro-cristalline hanno migliori proprietà meccaniche a parità di peso, migliore rigidezza e buone caratteristiche di resilienza. Svariate analisi FEM sono state condotte considerando i provini costituiti dai meta-materiali tenendo anche conto dei vari difetti come porosità e vuoti. Tutte le difettosità derivanti dall’utilizzo dell’additive manufacturing sono state considerate utilizzando il modello di danneggiamento duttile di Gurson Tveergard Needleman (GTN). Il modello GTN nell’analisi FEM è stato comparato con test sperimentali in compressione e in flessione a tre punti. L’introduzione di una sezione nel piano medio nel modello di flessione a tre punti (spessore uguale al diametro della struttura), ha portato a un miglioramenti dei risultati.Tutti gli esperimenti sono stati campionati mediante l’utilizzo della digital image correlation (DIC), confrontata poi con la massima deformazione nella sezione di massima freccia e con i risultati dei provini portati a rottura.Un’analisi tomografica è stata utilizzata per analizzare l’effettivo reticolo cristallino presente nel reticolo f2-BCC e f2-FCC-L. La geometria, la dimensione della struttura, la porosità, i vuoti e anche l’analisi del modello sperimentale del reticolo f2-BCC sono stati analizzati utilizzando la tomografia. Successivamente il modello reale è stato migliorato considerando le limitazioni tecnologiche.Infine, l’effetto dinamico è stato studiato tramite modelli FEM, per capirne le proprietà, utilizzando il modello GTN. L’effetto dinamico è evitato tramite l’aumento del tempo, quindi tramite la riduzione del coefficiente di carico a parità di spostamento.This work study is majorly about lattice structures (f2-BCC and f2-FCC-L), by means of additive manufacturing for AlSi10Mg using selective laser melting (SLM). These two micro lattice structures have better strength to weight ratio, greater stiffness, and good energy absorption characteristics. FEM analysis is done considering meta materials to build the sample considering the various defects like voids and porosity. All the defects from additive manufacturing are considered while using ductile damage model of Gurson Tveergard Needleman (GTN). GTN model in FEM analysis is made and compared with experimental test for three-point bending and compression analysis. By introducing a middle plane section in the three-point bending model (thickness equal to the diameter of strut) improves the result. All the experiments are captured through digital image correlation (DIC) to check whether the strain concentration of strut in the maximum displacement area and the results of the ruptured experimental samples is compared with DIC results. Tomography is used to analyze the real lattice model of f2-BCC and f2-FCC-L. The geometry, strut dimension, porosity, voids as well as the analysis of the experimental f2-BCC model is analyzed using tomography. Thus, the real model has been improved considering manufacturing limitations. Finally, the dynamic effect in FEM model is studied to understand it’s behavior by using the GTN model. The dynamic effect is avoided by increasing the time thus reducing the load rate with constant displacement
Statistical options: Crash resistant financial contracts based on robust estimation
No full textWe propose a class of European-type options, which is named here as statistical options, utilizing robust location estimators from the statistics literature. The main motivating objective is to protect the buyer of a call option against a sudden drop in the security price or a put option against a sharp upward move. The vast literature on the asymptotics for the location estimator can be called upon to accurately approximate the prices of these options, when the price formulae are not obtainable in closed form. The statistician's eternal quest for robust estimators which are highly efficient under normality finds here another reason. A notion of limit loss option emerges as a special case, possessing practical appeal. The pricing of the options is carried out under the popular Black-Scholes model. A theory based on the jump diffusion processes ascertains that these robust options manage to nullify the effect of jump arrivals (or that of just the negative ones) in a limiting sense. Finally, a notion of ratio hedging is proposed for the statistical options.European stock options Black-Scholes model Robust location estimators Median Trimmed means Hodges-Lehman estimator Crash resistant options Saddlepoint approximation Hedging
Reducing the patients-at-risk (PaR) in a response-adaptive trial: A numerical study
No full textThis article investigates the dichotomy between higher statistical power and higher allocation to better treatment in an ethical-optimal response-adaptive design. Although many response-adaptive designs in the literature promise higher allocation to the superior treatment, this is not always guaranteed due to the variability of the designs. A new criterion for evaluating response-adaptive designs, motivated by the value-at-risk measure, is proposed to address this problem. We also provide an illustration of applying this criterion in a real clinical trial
Topics in statistical finance
No full textThis thesis is divided into three parts. The first part investigates the presence of long term dependence in stock price data via a permutation test based on the correlation structure of the underlying stock prices. These tests reveal the short term nature of stock price dependence structure. The second part extends
Ramprasath and Singh(2007)'s `statistical options' to define a group of American type options based on robust estimators of location. The payoff functions of these path dependent options are based on a new set of stochastic processes which are defined using various robust estimators of location. The asymptotic distributional behavior of these new processes is ascertained which in turn is used in pricing
the options. Markov Chain Monte Carlo (MCMC) methods were used to compute the prices of the statistical options. The third part explores a stock price model parameter estimation problem and interprets a growth rate parameter.Ph.D.Includes bibliographical references (p. 81-83)
ANVILS-VOCE: ANova-based Varying Inner-Loop Size estimation of Variance of Conditional Expectation
No full textAnalysis of Variance (ANOVA) is a popular method to infer, based on the sampled data, whether the true means of a set of subpopulations differ from each other. The variance of conditional expectation (VOCE) is the variance of these effects in sub-populations, and this is estimated by sampling a sub-population of size nk, for each sub-population labeled k, and by sampling K such sub-populations in the experiment. For the general case of varying nk, it is unknown what the variance of the VOCE estimator is, though it is known for the special case nk=n, n≥2 for all k∈1,2,…,K as derived in the literature. The following derivation settles the former question and is of value in situations where sampling has constraints or only a skewed sampling budget is available. Our first application is with regard to the decision of whether samples from pilot simulation can be included in the regular simulation to estimate VOCE. The second application is an estimation technique where the estimate of optimal inner-loop size n* can be updated throughout the duration of simulation. We demonstrate with these 2 applications where we observe a 20% reduction in the variance of the VOCE estimate, when the proposed method is applied.</p
