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The objective of this master’s thesis is to describe the causal effect of ever being imprisoned on the probability of having human immunodeficiency virus among people who inject drugs. Here, we meta-analyse individual-level patient data that has been collected throughout Europe. Firstly, we provide an overview of the individual patient data and the process of merging the data sets into a complete analysis data set. Subsequently, we provide an overview of the bias reduction and causal inference and modelling methods such as propensity score matching and generalised linear mixed model. Finally, the thesis focuses on applying these practices on the merged data set. As a result, the thesis confirms the existence of a risk-increasing effect of ever imprisonment to the probability of having human immunodeficiency virus.

The purpose of this thesis is to explore stochastic volatility models to price American and European options. The two methods used are both based on a quadrinomial tree, but the first uses an Ornstein-Uhlenbeck process and the Monte Carlo method with a quadrinomial recombining tree and the second uses the Heston model and a tree-based approach that combines a grid and bilinear interpolation to estimate the option price. The thesis is split into four chapters. In the first chapter, it gives an overview of options, option pricing models, and numerical methods. The second chapter discusses the quadrinomial recombining tree, and the third presents the tree-based approach that uses a grid and bilinear interpolation. Finally the fourth, presents the results of both methods and then compares their performance and flexibility.

Magistritöö eesärk on tutvustada pseudovaatluste kasutamist elukestusanalüüsis. Pseudovaatlused on jackknife meetodil arvutatud hinnangud üleelamistõenäosusele, mis näitavad ühe vaatluse mõju valimi keskmisele, võttes arvesse andmetes esinevat tsenseerimist. Töö teoreetilises osas tehakse ülevaade elukestusanalüüsi mõistetest ja meetoditest, keskendudes Coxi võrdeliste riskide mudelile. Seejärel tutvustatakse pseudovaatlusi ja kolme pseudovaatluste arvutamise juhtu: hinnangut üleelamistõenäosusele, hinnangut tõkestatud keskmisele elueale ja konkureerivate riskide kumulatiivsele avaldumisele. Töö praktilises osas kasutatakse Coxi võrdeliste riskide meetodit ja pseudovaatlusi, et hinnata liiklusõnnetuse tagajärjel tekkinud ravikulude hüvitamise kestust mõjutavaid tegureid.

Töö eesmärk on uurida nõudmiseni hoiusele pakutavate intresside sõltumist 6-kuulisest euriborist ja 6-kuulise euribori swap’i määrast. Selleks uuritakse ARIMAX tüüpi mudelite moodustamist ja kointegratsiooni hoiuse intresside ja turumäärade vahel. Lisaks moodustatakse mudelid naturaallogaritmi ja hüperboolse siinuse pöördfunktsiooni abil transformeeritud aegridadele. Töö on motiveeritud krediidiasutuste vajadusest intressiriski hinnata, kus intressirisk on ettevõtte risk saada kahju intressimäärade muutumisest. Hoiuse intresside prognoosimine turumäärade abil on oluline sisend intressiriski hindamise protsessi.

Time series data are sometimes affected by multiple cycles of different lengths. There can be a weekly cycle (better sales on Fridays), a monthly pattern (better sales at the beginning of the month as people have more cash after payday), and the effects of calendar seasonality (more tourists during summer, so better sales) might be present also. How to model multiple seasonality in one model? In this thesis, one could compare, for example, TBATS models (which allow multiple seasonalities) to alternative approaches.

Mobile positioning data is a promising source for investigating people’s activity patterns. People regularly visit locations that have different functions to them. Locations with similar activity patterns can be distinguished from the data based on people’s calling activities. The problem with assigning meaning to these locations in the data is limited information about the person and access to ground truth data. The thesis proposes a method to profile locations and assign meanings to differently behaving location groups. In the course of the work, various features are added to the location points by means of which they are classified. Additionally, an expert’s opinion was considered to provide input for the classes.

The thesis examines the validity of the Capital Asset Pricing Model (CAPM). CAPM includes components to quantify the systematic risk of assets/portfolios and evaluate the performance of assets concerning the related market. The basis of this method is rooted in the analysis of mean-variance (return and risk), which is part of Modern Portfolio Theory (MPT). The two main components of this model are beta and Jensen’s alpha. Based on the degree of risk aversion of investors, beta helps investors construct a well-diversified or less risky portfolio, the most challenging aspect of this model. Alpha evaluates the performance of assets, even portfolio managers’ performance. We first present the concepts and mathematical foundation of CAPM and then explore the validity of the model in two different markets: the Tehran Stock Exchange (TSE), 30 selected companies, and the New York Stock Exchange (NYSE), 30 companies constituted in the Dow Jones Industrial Average (DJIA). The behavior of these markets was opposite of each other, but they both confirmed CAPM. To improve our estimation, we used the Fama-French three-factor model, which improved asset pricing in both data sets, and finally, we added the illiquidity factor to the Fama-French three-factor model, which added a bit more improvement to the Fama-French model.

The objective of this master’s thesis is to find an appropriate time series model to forecast the volume of private customers’ savings deposits of one undisclosed Swedish financial institution. Models such as Holt, Holt-Winters, ARIMA and ARIMAX are fitted to the data under analysis. The best performing model is ARIMA showing approximately 20% lower error measures during the out-of-sample test period compared to the best ARIMAX models.

Magistritöö eesmärk on tutvustada levinumaid Bayesi segumudeleid ja vastavaid Gibbsi valikul põhinevaid meetodeid tiheduse ligikaudseks hindamiseks.Samuti illustreeritakse meetodite tööd arvutisimulatsioonide abil.

Käesoleva magistritöö eesmärgiks on välja selgitada otstarbekad meetodid krediidiriski hindamiseks, kui argumenttunnused on valdavalt kategoriaalsed. Töös võrreldakse nelja erinevat prognoosimudelit – logistilist regressiooni, LASSO regressiooni, klassifitseerimispuud ning gradient boosting algoritmi. Töös kasutatav andmestik sisaldab infot väikelaenu saanud isikute kohta ning uuritavaks tunnuseks on laenu staatus, mis kirjeldab, kas laen on krediidiasutusele tagastatud või mitte.