Browsing by Title

Liikunnan väheneminen on nykymaailmassa valtava terveysongelma, jonka vaikutukset näkyvät jo lisääntyneinä terveydenhoidon kuluina. Aiempi tutkimus on antanut viitteitä siitä, että liikuntamahdollisuuksien hyvä saavutettavuus lisää liikunnan määrää. Laajalla ja hyvin saavutettavalla liikuntapaikkatarjonnalla voikin olla tärkeä rooli väestön säännöllisen liikuntaharrastuksen tukemisessa. Jos liikuntapaikalle matkustamiseen menee liikaa aikaa, saattavat muut arjen toiminnot mennä liikunnan harrastamisen edelle. Erityistä huomiota tulisi kiinnittää lasten ja nuorten liikuntamahdollisuuksiin, sillä lapsuusajan liikunnallisuudella saavutettuja terveyshyötyjä ei täysin voi korvata aikuisena omaksutulla aktiivisella elämäntavalla. Tutkimuksen toimeksiantajana toimi Helsingin kaupungin liikuntavirasto, joka nykyään on osa kulttuurin ja vapaa-ajan toimialaa. Tutkimusasetelmassa korostuukin palveluntuottajan näkökulma ja se, että julkisten palveluiden olisi oltava oikeudenmukaisella tavalla sijoitettuja. Tutkimuksessa tarkastellaan Helsingin liikuntapalveluverkon saavutettavuuden nykytilaa monen eri liikuntapaikkatyypin osalta eri oikeudenmukaisuuden näkökulmista. Tutkimusasetelman avulla on mahdollista arvioida erilaisten tarkastelutapojen soveltuvuutta kunnalliseen palvelusuunnitteluun. Tutkimusmenetelmänä olivat matka-aikoihin perustuvat saavutettavuuslaskennat liikuntapaikoille asutuista 250 x 250 metrin ruuduista. Laskennoissa huomioitiin yksityisautoilu, joukkoliikenne ja kävely riippuen kyseessä olevasta liikuntapaikkatyypistä ja sen palveluprofiilista. Analyyseja oli kolmenlaisia: 1) matka-aikalaskennat koko väestön osalta arkena kello 17.30–18.30, 2) matka-aikalaskennat samaan aikaan ruuduista, joissa asuu paljon 7-20-vuotiaita ja 3) matka-aikojen ja kokonaismatkaketjujen vertailu, kun harjoitusaika ja -paikka on ennalta määrätty. Hyväksyttävänä enimmäismatkustusaikana pidettiin kirjallisuuteen perustuen 30 minuuttia. Tulosten perusteella voidaan liikuntapalveluverkon todeta olevan Helsingissä pääasiassa hyvin saavutettavissa myös joukkoliikenteellä ja jopa kävellen, vaikka henkilöautosaavutettavuus onkin edelleen omaa luokkaansa. Tulokset osoittavat lisäksi, että saavutettavuus on väestön painopistealueet huomioiden parempi, kuin vain alueellisessa tarkastelussa. Myös 7-20-vuotiaat ovat sijoittuneet enimmäkseen hyvän saavutettavuuden alueille. Kolmas analyysi puolestaan todistaa, että erot autoilun ja joukkoliikenteen välillä ovat temporaalisessa tarkastelussa merkittäviä. Kokonaisuutena tutkimus osoittaa, että palvelusuunnittelua varten on tarkasteltava saavutettavuutta moni eri asia huomioon ottaen, jotta oikeudenmukaista palveluiden sijoittelua koskevat päätökset voidaan tehdä tietoperustaisesti. Saavutettavuusanalyysien avulla voidaan arvioida uusien liikuntapaikkojen sijainteja siten, että ne tukisivat väestön säännöllistä liikuntaharrastusta ja aktiivista elämäntapaa.

Työssä käsitellään opetuspelejä ja motivaatiota matematiikan opetuksessa. Tarkastelun kohteena ovat motivaatiota lisäävien seikkojen ja pelien ominaisuuksien yhtenevyydet. Apuna käytetään kaupunkisuunnistusta ja mobiiliteknologiaa yhdistävää peliä, jonka sisältö laadittiin lukion lyhyen matematiikan opetukseen sopivaksi. Pelistä saatiin käytännön kokemuksia peliä johtamalla ja kyselyiden avulla sitä pelanneelta lukioryhmältä. Työssä pohditaan tämän pelin mahdollisuuksia matematiikan opetuksessa ja motivaation lisäämisessä. Luku 2 alkaa pelejä käsittelevällä osuudella, jossa kerrotaan, minkälaisia ominaisuuksia peleillä on ja mitä nämä ominaisuudet tarkoittavat pelaajan näkökulmasta. Pelejä voidaan kutsua organisoiduksi leikiksi: niillä on leikinomaisia piirteitä, mutta niiden säännöt ovat leikkiä selkeämmät. Lisäksi peleissä on jokin tavoite, johon pääsemistä edeltävät erilaiset haasteet tai vastustajat. Leikin tavoin peleissä on vuorovaikutusta, joka voi olla ihmisten tai ihmisen ja tietokoneen välistä. Pelit myös kertovat tarinoita, olivat ne sitten monimutkaisia juonia tai kahden henkilön välistä kilpailua. Luvussa 2 käsitellään pelien lisäksi motivaatiota. Motivaatiota tutkittaessa etsitään vastausta siihen, miksi ihmiset toimivat niin kuin toimivat. Työssä huomio keskittyy siihen, kuinka motivaatiota voidaan lisätä. Tätä tarkastellaan sen kannalta, millaisen toiminnan on todettu olevan houkuttelevaa. Esiin nousee neljä ominaisuutta: onnistumiskokemuksien tuottaminen, uteliaisuuden herättäminen, itseilmaisuun kannustaminen ja ihmissuhteiden vaaliminen. Luvussa 3 käydään lyhyesti läpi työn ja sitä varten pelatun pelin tausta. Luku 4 jatkaa luvun 3 lyhyestä taustaselvityksestä kertomalla tarkemmin pelin kulusta ja säännöistä. Luvussa 5 käsitellään pelistä saatuja kokemuksia, joita kerättiin kyselyillä, joihin vastasivat peliä pelanneet opiskelijat sekä peliä vetämässä ollut opettaja. Opiskelijat ja opettaja vastasivat yhteen kyselyyn ennen peliä ja toiseen pelin jälkeen. Kyselyjen perusteella opiskelijoilla oli pelistä melko positiivinen kuva niin ennen peliä kuin sen jälkeenkin. Opettaja suhtautui ennen peliä hiukan epäileväisesti, mutta pelin jälkeen hänen mielikuvansa olivat muuttuneet positiivisemmiksi. Vastauksista todetaan löytyvän seikkoja, joiden perusteella voidaan arvella opiskelijoiden nähneen pelissä houkuttelevan tekemisen ominaisuuksia. Pelin käytännön onnistumista tarkastellessa havaitaan tämä sama tulos. Luvussa 6 pyritään yhdistämään motivaation ja pelien teoriat pelatun pelin kanssa. Tarkastelun kohteena on se, kuinka hyvin työtä varten pelattu peli onnistui toteuttamaan houkuttelevan tekemisen ominaisuuksia. Kaikkien näiden ominaisuuksien toteutumisen mahdollisuuksia voidaan kasvattaa. Työtä varten pelattu peli ja pelit yleensä todetaan perustelluksi osaksi matematiikan opetusta. Erityisesti pelien arvellaan lisäävän opiskelijoiden innostusta osallistua tunnin kulkuun ja näin saavan myös lisää mahdollisuuksia innostua matematiikasta.

The changes in our society have had their ramifications in the sense of community in neighborhoods, the latest big social change being the fast alteration of the media environment. Digital forms of communications allow people to communicate almost instantly all over the world. Yet people still tend to form social ties locally, and a growing interest to local themes has been on the rise. The aim of this case study was to find out which underlying housing and socio-economic factors affect the sense of community in neighborhoods, sense of community in areal Facebook groups and the activity of use of these groups, and if there is overlapping in the factors affecting these. The other aim was to examine if communality in areal Facebook groups or the activity of their use increases sense of community in neighborhoods in Helsinki. The research was descriptive, and the objective was not necessarily to make generalizations to the whole study population. Two differing views have shaped the grand theories of sense of community in neighborhoods. In the first wave, there was a division between idealizing the feudal communities, where a strong dependency of neighborly relationships was a given and the relationships of the urban neighborhoods, where residents were seen as isolated and unsatisfied. The changing society shifted the view to examining relationships as a personal network and the form of communities in the overlapping of these networks. These two views differ most importantly in their views of the meaning of distance to social relationships, and the importance of neighborly relationships in general. In the Internet era relationships can be seen to be formed in networks, but neighborhoods and physical proximity still carry a meaning to local relationships. Two different research areas, in terms of common housing types and the amount of children in families, were chosen from neighborhoods in Helsinki; the northern study area around Paloheinä, Pakila and Torpparinmäki, and the southern area around Kallio and Vallila districts. A questionnaire was sent to three different areal Facebook groups and the total amount of responses received was 335. Sum variables were formed to indicate the sense of community among the respondents, sense of community in their areal Facebook group and the use activity of that Facebook group. These variables were then further analyzed statistically and compared to each other and the respondents’ background factors. The responses split up quite evenly between the two study areas, and the background information reported by the respondents reflected the same factors that these areas were chosen by. All the sum variables correlated positively with each other, thus indicating that those who had a greater sense of community in their neighborhood also possessed a greater sense of online community in their areal Facebook group. The respondents from the northern study area had altogether a higher sense of community, sense of community in the areal Facebook group, and a more active use of the group. The results reflected the ones from previous studies, as a higher sense of community was attached to older age, longer residence in the area, apartment ownership, having children in the family and living in a one-family house. Living in a one-family house was also attached to higher sense of community in the areal Facebook groups, as well as having children, long residence in the area and apartment ownership. According to the results in this case study, some of the same background factors produced a higher value in the sense of community in neighborhoods and the sense of community in the areal Facebook groups studied. These shared factors and the correlations between the sum variables indicate that higher sense of community in areal Facebook groups could lead to a higher sense of community in neighborhoods as well. Distance in relationship still possesses a meaning as neighbors form areal groups in social media that can develop into lively communities.

The topic of this thesis is participatory budgeting and its connection to the discussion between neoliberalism and participatory governance in the context of city development. Helsinki started its own model of participatory budgeting in 2018 and has pledged to continue the concept in the future. I examine whether Helsinki’s participatory budgeting has the potential to support the ideologies of neoliberalism or participatory governance. In practice, I am exploring the views from the city government and active members of Helsinki’s neighborhood associations. Neighborhood associations had a significant role in the original participatory budgeting of Porto Alegre. I used interview and qualitative survey to collect my data. Neoliberalism has influenced the inequality between regions and the so-called crisis of democracy. Direct involvement of citizens is seen as a solution to these problems. Neoliberalism and participation have a paradoxical relationship: they have received similar criticism. In participatory governance participation means deliberative decision-making based on exchange of knowledge, but in neoliberalism participation can be a rhetoric tool to cover up actual decision-making or a city branding technique. Porto Alegre’s original model of participatory budgeting is seen as a part of participatory governance, but many of the international models seem to be more compatible with neoliberal ideology. The city government has not reserved enough resources to the participatory budgeting. The execution was rushed and showed signs of rationalization. According to the interview and the qualitative survey, inequality between regions might be the downfall of Helsinki’s participatory model. The active members of neighborhood associations see the benefits of participation budgeting but only from the perspective of certain regions. Currently, Helsinki’s participatory budgeting works better as a branding technique than as a method of decision-making. It seems to be more compatible with neoliberalism than participatory governance.

Helsingin puistoissa on aikaisemmin tutkittu maaperän pilaantuneisuutta, mutta tutkimukset ovat lähinnä keskittyneet Helsingin keskustan alueelle. Tässä tutkimuksessa maaperänäytteitä kerättiin 50:stä eri puistosta koko Helsingin alueelta, lukuun ottamatta Östersundomia, jonka lisäksi näytteitä otettiin myös neljältä Helsingin edustan saarelta ja neljältä uimarannalta. Helsingin puistoissa, saarilla ja uimarannoilla As-, Cd-, Co-, Cr-, Cu-, Ni-, Pb-, V- ja Zn-pitoisuudet olivat pääasiassa alhaiset, mutta ohjearvoja ylittäviä pitoisuuksia löytyi Eugen Schaumanin puistosta, Kumtähdenkentältä, Paloheinänhuipulta (täyttömäki), Haaganpuistosta ja Munkinpuistosta. Alueellisesti alhaisimmat metallipitoisuudet olivat ItäHelsingissä, Helsingin edustan saarilla ja uimarannoilla. Työn tarkoituksena oli myös arvioida pXRF-laitteen soveltuvuutta metallipitoisuuksien mittaamiseen maaperän orgaanisesta pintakerroksesta ja vertailla kahden eri raekoon metallipitoisuuksia toisiinsa: < 2 mm ja < 0,06 mm. Menetelmien vertailussa pXRF-laite antoi korkeammat arseeni-, kromi-, kupari-, lyijy-, vanadiini- ja sinkkipitoisuudet, kuin ICP-MS-menetelmä. Parhaiten pXRF-laite soveltui kupari, sinkki ja lyijypitoisuuksien mittaamiseen, joten kentällä käytettävää pXRF-laitetta voidaan siis hyvin käyttää näiden aineiden kohdalla, mutta todelliset pitoisuudet tulisi tarkistaa laboratoriossa käytettävillä laitteilla, kuten esim. ICP-MS:llä. Arseeni- ja kromipitoisuuksien mittaaminen pXRF-laiteella osoittautui vaikeaksi, sillä näytteiden pitoisuudet olivat etenkin < 2 mm:n raekoossa alle laitteen määritysrajan. Kromissa raekoko vaikutti pXRF-laitteen mittaamiseen, sillä hienoaineksessa R2 oli 0,91, kun puolestaan < 2 mm:n raekoossa se oli 0,46. Lisäksi nikkeli-, kadmium- ja kobolttipitoisuudet olivat kaikki alle pXRF-laitteen määritysrajan, joten tuloksia näille aineille ei saatu pXRF-laitteella. Suomessa maaperän pilaantuneisuutta tutkitaan < 2 mm:n raekoosta, mutta maa-aineksen raekoon on huomattu vaikuttavan näytteen metallipitoisuuksiin. Tässä tutkimuksessa arseeni-, kromi-, kupari-, lyijy-, vanadiini- ja sinkkipitoisuudet olivat korkeampia hienoaineksessa, kuin < 2 mm:n raekoossa. Tämän lisäksi lyijy, sinkki ja kadmium korreloivat parhaiten < 2 mm:n ja < 0,06 mm:n raekoossa.

The aim of the thesis was to study the socioeconomic structure of Helsinki and bring new and relevant information to the discussion about the future of the Helsinki region. Socioeconomic differentiation in Helsinki is a widely studied subject. The focus, however, has mostly been on statistical region or grid cell based analyses. In this study the socioeconomic structure was, for the first time, linked with transport nodes. Train and metro station areas are in Helsinki often functional and commercial centers of their districts and as transport nodes they offer good connections to rest of the region. In this study the train station areas were defined as areas within a 600 meter radius buffer from the train/metro platform. Socioeconomic structure was defined by four independent variables: percentual amount of highly educated population (= university or applied university diploma), employment rate, median income of the workforce and the percentual amount of population with first language other than Finnish or Swedish. Values of the station areas were set against the values of the whole city as well as against the values of Helsinki's districts and major districts and the values of the surrounding 300 meter zone of the station area itself. The station areas were divided into quartiles based on their rank within each variable. These quartiles were then used to create a combined categorization which shows the relative socioeconomic level of each station area when compared to the surrounding city. The data of the thesis comprised of large amount of GIS data from several different places. The most central data was from SeutuCD'09 by Helsinki Region Environmental Services Authority HSY and from Ruututietokanta grid database provided by Statistics Finland. In addition to the two focal data sources also some GIS data by the city of Helsinki's planning and real estate departments was used. Station areas were categorized in the thesis in two separate ways: based on functionality and on the diversity of built environment. In order to measure the diversity of the built environment an application was created that used Simpson's diversity index used mostly in biological studies. Urban diversity has not been widely studied in terms of GIS data based indexes before. Socioeconomic differentiation can be clearly noticed in Helsinki's station areas. Some station areas are clearly socioeconomically strong regions where as some station areas, especially in the lowest quartile, are showing worrying results. The findings reflect earlier research results about the socioeconomic differences within Helsinki. The station areas with lowest values are located mostly in eastern, northeastern or northwestern parts of Helsinki, where as the station areas with highest values are generally located either in downtown or in the region between the urban core and the apartment building suburbs built in 1960's and 1970's. Regardless of the comparison level proximity to the station appears to have negative impact on the socioeconomic level of an area. Distance to the city center correlates with the socioeconomic situation of a station area. The closer the station is to the urban core, the higher the socioeconomic status. When comparing the relative socioeconomic status of the station areas to surrounding urban regions, the station areas with highest relative status are located in the region between the city center and the furthest suburbs and have been inhabited for a relatively long time. Recent development shows that the station areas with slowest growth rates or even declining rates are mostly the ones that have already been areas of low socioeconomic status. The results corroborate earlier findings about the linkage of subsidized and owner-occupied housing to the socioeconomic structure of a given region. In case the goal is to maintain the socioeconomic balance of Helsinki the ownership of new housing plays a crucial role in preventing the segregation development.

Helsinki is a densely built and populated Finnish city, which faces special land use management needs due to its capital status. The expected population growth causes pressure to the amount, quality and regionally equal distribution of the city´s recreation areas. The Recreation Opportunity Spectrum (ROS) method was developed to solve recreation areas´ management problems caused by a rapid increase of recreation areas´ users in United States. The ROS method developers believed that by offering diverse recreation possibilities the injurious environmental and recreational impacts caused by the increase of the users would be minimized. The method is based on an idea whereby a high quality recreation experience is best ensured by offering diverse recreation possibilities. According to the method´s theory, a recreation area´s physical features determine the recreation activities and experience possible. The purpose of the thesis is to explore the diversity of summertime outdoor recreation possibilities in Helsinki by using the ROS method. By examining the recreation conditions´ state of development or naturalness I will form a spectrum representing different recreation opportunities in Helsinki. I will also explore the main arguments for promoting diverse recreation possibilities according to the research literature. The materials of the analyzes consisted of open spatial data determining recreation areas´ physical environment, social and managerial settings. Variables of recreation areas´ physical environment consisted of the size of the area and the impacts of the surrounding land use. The social conditions of recreation areas were examined through their theoretical population pressure. The impression of naturalness, access to the recreation areas and their service facilities determined the managerial conditions. The variables were analyzed by GIS methods, most importantly by distance analyzes. The importance of diverse recreation possibilities is rationalized by three main arguments in the research literature. The diversity of recreation possibilities is justified most importantly by the high diversity of recreationists. Also the so called “problem of relying on averages” and the realization of environmental justice in recreation are key arguments to promote diverse recreation possibilities. The actual diversity of Helsinki´s recreation possibilities is low on a city level since most of the recreation areas´ land area has both natural and urban features according to the different variables. The edges of the ROS scale are strongly represented in the study area. The most natural recreation areas of Helsinki are located in Östersundom, Isosaari and Pikku Niinisaari. The most urban recreation possibilities of the city can be found from the southern parts of Central Park and from small and fragmented recreation areas typically close to the main roads and railway line. It is to be expected that the most developed recreation areas in Helsinki will face increasing population pressure in the near future. It is also likely that a considerable part of the current environments offering most natural recreation possibilities will develop more urban, when the remaining natural possibilities will centralize in to the archipelago. The decrease of environments offering natural recreation possibilities may increase the recreation use of surrounding cities´ natural recreation areas. There are already some references of the trend in Helsinki.

The aim of this study is to examine what kind of mental images are attached to twelve city districts in Helsinki. More accurately put the research questions are 1) to find out how images are portrayed when writing about them in newspapers or spoken about by real-estate agents. 2) What kind of effect mental images has on people and 3) what kind of discursions affects those images. The districts are chosen so that they represent well different areas in Helsinki from their socio-economic and cultural background, as well as architecturally. These districts are Kruununhaka, Töölö, Kallio, Haaga, Oulunkylä, Paloheinä, Viikki, Malmi, Jakomäki, Herttoniemi, Mellunmäki and Östersundom. The research data contains real-estate agents' interviews and articles from Helsingin Sanomat. Real-estate agents provide an interesting viewpoint to different districts with their expertise of neighborhoods and clients. Helsingin Sanomat, for one, portrays the word of media in this research. The influence of media is very powerful, even so that the image it gives of unknown districts becomes 'the truth' of them. The newspaper data contains over 300 articles of different city districts and matters that are associated with mental images of those districts. The real-estate agents' data consist of 43 answers to internet based survey questionnaire. Based on the results it turns out that the real-estate agents are very familiar with almost every district, especially those located in downtown. Most poorly they know about the image of Östersundom, which has been merged to Helsinki most recently. Downtown districts' mental images are perceived positively, as also is the case with residential district Paloheinä and green functionalistic suburb Haaga. The mental images of areas located in eastern or north-western Helsinki, such as Malmi, Jakomäki and Mellunmäki, are perceived most negatively. The impression that newspaper articles give is the same. Articles about those districts very often contain negative expressions even though during the year 2014 aspect of writing has been more positive and has given more peaceful and better image of districts that have bad reputation. The data of real-estate agents' questionnaires also imply that mental images have very great significance for people, especially for the citizens of Helsinki when they are making decisions where to move. Many mental images are also stereotypical and dated. Based on the results can be discovered that mental images are composed by many factors. Firstly, architecture and building time have great influence especially to techno-rationally built areas. They usually have week images for example because of the hard times Finland was going through during the building time. Areas that were built during Empire, Jugend or Functionalistic eras are very popular and perceived positively. They are commonly portrayed by good historical matters. New districts are perceived mostly positively and are sometimes linked to images that are created during city planning. Secondly, geographical location has prejudiced influence on image. Location in eastern or north-western Helsinki dramatically pushes the mental image towards negative conceptions even though it was unsuitable. Thirdly, poverty discursion stigmatizes disadvantaged areas with slummy things such as alcoholism and disquietude. Mental images are altered very slowly but the change is important for example for the city of Helsinki, which is actively trying to create plans for making all city districts' images better.

The Helsinki City Plan Vision 2050 perceives urban parks as its citizens’ living rooms that offer a setting for diverse urban life. The definition of a living room highlights the notion of “hanging out”, sharing space and possibilities for social encounters. In a densifying future urban environment, the significance of urban parks as multifunctional centres of urban life and high quality recreation areas continue to grow. The aim of this thesis was to discover what characterizes Helsinki’s urban parks as public spaces, and to investigate the role they can have in enhancing the lively city. Based on human geography, this thesis hoped to examine the place meanings that urban dwellers attach to urban parks. This research emphasizes the importance of residents’ experiences in knowledge production and is especially interested in the world of experiences that evolve from urban parks as social environments. The thesis was written as part of a European Union funded project GREEN SURGE which in Finland is coordinated by the Department of Environmental Sciences at the University of Helsinki. As a research group, we collected interview and observation field data based on the project guidelines in 12 urban parks in Helsinki in summer 2015. In total, we received 596 interviews. The most popular motivations to use urban parks included relaxing, hanging out, recreation and enjoying the sunny weather, whereas the significance of nature in user motivations was lower. Activities mentioned as social (being together, having a picnic etc.) covered about one fourth of all motivations to use the parks. Park users who arrived for social reasons tended to stay in parks longer and enjoyed the human environment - company and atmosphere - more often. Otto-Iivari Meurman Park in Käpylä turned out to be superior from the point of view of community spirit and lively social atmosphere, which was mainly due to the little café inside the park. In total, 65 % of park users stated the park as very important. The sources of importance were versatile, but close location and physical green environment were highlighted. On the parks’ level, results showed that a park can be a social public space stimulating the lively city without a deep sense of place from park users. It seems that a park can be important to its user only because the space offers the right opportunities of use and pleasant human environment or atmosphere. The result in part challenges the traditional visions of human geographers over the differences in the meaning of space and place. This research concluded that the urban parks of Helsinki cannot be defined as one type that fulfills same functions in urban space. As social public spaces, other parks are successful and “work” - others unsuccessful and do not work. The parks that were defined as quality social spaces were successful e.g. due to their location, design, multifunctionality, services and identity formation, and they attracted users to stay in the park. In the light of this research, successful urban parks have the potential to enhance the lively city and support the Helsinki City Plan Vision to create a good living environment for all.

Vakuutussopimusten tappion arvioiminen on tärkeää vakuutusyhtiön riskienhallinnan kannalta. Tässä työssä esitellään Hattendorffin lause vakuutussopimuksen tappion odotusarvon ja varianssin arvioimiseksi sekä sovelletaan sen tuloksia monitilaisella Markov-prosessilla mallinnettavalle henkivakuutussopimukselle. Hattendorffin lauseen nojalla ekvivalenssiperiaatteen mukaan hinnoitellun vakuutussopimuksen erillisillä aikaväleillä syntyneiden tappioiden odotusarvo on nolla, ja tappiot ovat korreloimattomia, jonka seurauksena tappion varianssi voidaan laskea erillisillä aikaväleillä muodostuneiden tappioiden varianssien summana. Työn soveltavana osana simuloidaan Markov-prosesseja sopivassa monitilaisessa mallissa mallintamaan henkivakuutussopimuksien realisaatioita. Tutkitaan, onko simuloitujen polkujen tuottamien vuosittaisten tappioiden keskiarvo lähellä nollaa, ja onko koko sopimusajan tappioiden varianssin arvo lähellä summaa vuosittaisten tappioiden variansseista. Lisäksi lasketaan simulaation asetelmalle Hattendorffin lauseen avulla teoreettiset vastineet ja verrataan näitä simuloituihin arvoihin. Vakuutussopimus pitää karkeasti sisällään kahdenlaisia maksuja: vakuutusyhtiön maksamat korvausmaksut ja vakuutetun maksamat vakuutusmaksut. Vakuutussopimuksen kassavirta on jollain aikavälillä tapahtuvien vakuutuskorvausten ja -maksujen erotuksen hetkeen nolla diskontattu arvo. Vastuuvelka on määrittelyhetken jälkeen syntyvän, määrittelyhetkeen diskontatun, kassavirran odotusarvo. Vakuutussopimuksen tappio jollain aikavälillä määritellään kyseisen aikavälin kassavirran ja vastuuvelan arvonmuutoksen summana. Kun määritellään stokastinen prosessi, joka laskee tietyllä hetkellä siihen mennessä kumuloituneet kustannukset sekä tulevan vastuuvelan nykyarvon, voidaan tappio ilmaista tämän prosessin arvonmuutoksena. Kyseinen prosessi on neliöintegroituva martingaali, jolloin Hattendorffin lauseen tulokset ovat seurausta neliöintegroituvien martingaalien arvonmuutoksen ominaisuuksista. Hattendorffin lauseen tulokset löydettiin jo 1860-luvulla, mutta martingaaliteorian hyödyntäminen on moderni lähestymistapa ongelmaan. Esittämällä monitilaisella Markov-prosessilla mallinnettavan sopimuksen kustannukset Lebesgue-Stieltjes integraalina, saadaan tappion varianssille laskukelpoiset muodot. Markov-prosessilla mallinnettavilla sopimuksille voidaan johtaa erityistapaus Hattendorffin tuloksesta, missä tappiot voidaan allokoida eri vuosien lisäksi eri tiloihin liittyviksi tappioiksi. Soveltavassa osiossa nähdään, että yksittäisinä sopimusvuosina syntyneiden tappioiden odotusarvot ovat lähellä nollaa, ja otosvarianssien summa lähestyy koko sopimusajan tappion otosvarianssia, mikä on yhtäpitävää Hattendorffin lauseen väitteiden kanssa. Simuloidut otosvarianssit eivät täysin vastaa teoreettisia vastineitaan.