>Magister Scientiae - MSc / Pensions are essentially the only source of income for many retired workers. It is thus critical that the pension fund manager chooses the right type of plan for his/her workers.Every pension scheme follows its own set of rules when calculating the benefits of the fund’s members at retirement. Whichever plan the manager chooses for the members,he/she will have to invest their contributions in the financial market. The manager is therefore faced with the daunting task of selecting the most appropriate investment strat-egy as to maximize the returns from the financial assets. Due to the volatile nature of stock markets, some pension companies have attached minimum guarantees to pension contracts. These guarantees come at a price, but ensure that the member does not suffer a loss due to poorly performing equities.In this thesis we study four types of mathematical problems in pension fund management,of which three are essentially optimization problems. Firstly, following Blake [5], we show in a discrete time setting how to decompose a pension benefit into a combination of Euro-pean options. We also model the pension plan preferences of workers, sponsors and fund managers. We make a number of contributions additional to the paper by Blake [5]. In particular, we contribute graphic illustrations of the expected values of the pension fund assets, liabilities and the actuarial surplus processes. In more detail than in the original source, we derive the variance of the assets of a defined benefit pension plan. Secondly,we dedicate Chapter 6 to the problem of minimizing the cost of a minimum guarantee included in defined contribution (DC) pension contracts. Here we work in discrete time and consider multi-period guarantees similar to those in Hipp [25]. This entire chapter is original work. Using a standard optimization method, we propose a strategy that cal- culates an optimal sequence of guarantees that minimizes the sum of the squares of the present value of the total price of the guarantee. Graphic illustrations are included to in-dicate the minimum value and corresponding optimal sequence of guarantees. Thirdly, we derive an optimal investment strategy for a defined contribution fund with three financial assets in the presence of a minimum guarantee. We work in a continuous time setting and in particular contribute simulations of the dynamics of the short interest rate process and the assets in the financial market of Deelstra et al. [19]. We also derive an optimal investment strategy of the surplus process introduced in Deelstra et al. [19]. The results regarding the surplus are then converted to consider the actual investment portfolio per- taining to the wealth of the fund. We note that the aforementioned paper does not use optimal control theory. In order to illustrate the method of stochastic optimal control, we study a fourth problem by including a discussion of the paper by Devolder et al. [21] in Chapter 3. We enhance the work in the latter paper by including some simulations. The specific portfolio management strategies are applicable to banking as well (and is being pursued independently).

This thesis consists of an introductory part and four self-contained papers related to individual financial behavior and risk-taking in financial markets. In Paper [I] we estimate within-family and community social interaction effects upon an individual’s stock market entry, participation, and exit decision. Interestingly, community sentiment towards the stock market (based on portfolio outcomes in the community) does not influence individuals’ likelihood to enter, while a positive sentiment increases (decreases) the likelihood of participation (exit). Overall, the results stress the importance of accounting for family social influence and highlight potentially important differences between family and community effects in individuals’ stock market participation. In Paper [II] novel evidence is provided indicating that the influence from family (parents and partners) and peer social interaction on individuals’ stock market participation vary over different types of individuals. Results imply that individuals’ exposure to, and valuation of, stock market related social signals are of importance and thus, contribute to the understanding of the heterogeneous influence of social interaction. Overall, the results are interesting and enhance the understanding of the underlying mechanisms of social interaction on individuals’ financial decision making. In Paper [III] the impact of divorce ­­­on individual financial behavior is empirically examined in a dynamic setting. Evidence that divorcing individuals increase their saving rates before the divorce is presented. This may be seen as a response to the increase in background risk that divorce produces. After the divorce, a negative divorce effect on individual saving rates and risky asset shares are established, which may lead to disparities in wealth accumulation possibilities between married and divorced. Women are, on average, shown to not adjust their precautionary savings to the same extent as men before the divorce. I also provide tentative evidence that women reduce their financial risk-taking more than men after a divorce, which could be a result of inequalities in financial positions or an adjustment towards individual preferences.   Paper [IV] provides novel empirical evidence that gender identity is of importance for individuals’ financial risk-taking. Specifically, by use of matching and by dividing male and females into those with “traditional” versus “nontraditional” gender identities, comparison of average risk-taking between groupings indicate that over a third (about 35-40%) of the identified total gender risk differential is explained by differences in gender identities. Results further indicate that risky financial market participation is 19 percentage points higher in groups of women with nontraditional, compared with traditional, gender identities. The results, obtained while conditioning upon a vast number of controls, are robust towards a large number of alternative explanations and indicate that some individuals (mainly women) partly are fostered by society, through identity formation and socially constructed norms, to a relatively lower financial risk-taking.

This thesis explores the impact of two behavioural finance concepts, social psychology and psychology, on household financial decisions. Under social psychology, I investigate whether the variety and intensity of social engagement enhances stock market participation. With regard to psychology, I examine two behavioural biases. First, I investigate whether mental accounting influences portfolio choice in three asset classes and whether financial advice and housing tenure increase (decrease) the effects of mental accounts on portfolio choice. Second, I examine whether households’ self-reported housing wealth are anchored on published house price indices and whether anchoring bias is mediated by market information, mortgage refinancing decisions and social factors. The main contributions and findings in the three studies are as follows. First, although there is an elaborate body of research concerning the relationship between social engagement mechanisms and portfolio choice, most studies investigate specific mechanisms in isolation. Using three waves in the British Household Panel Survey (BHPS), I bring together five social engagement measures in one model and show that socially engaged individuals are more likely to participate in the stock market. Consistent with Granovetter’s (1973) theory of social networks I find that a weak tie (measured by social group involvement) has a positive effect on stock market participation whereas a strong tie (measured by talking to neighbours) has no effect. More trusting individuals are more likely to participate in the stock market, as are those who identify with a political party. In contrast, the degree to which religion is important appears to have little impact. These results are robust using different specifications. Overall, the results of this study demonstrate that the likelihood of stock market participation increases with the variety and intensity of social engagement. Second, despite the established theoretical underpinnings of mental accounting in behavioural portfolio theory (BPT) and recent extensions, not much is known about their implications in real life situations. I use a recent UK household survey, the Wealth and Assets Survey (WAS), which has comprehensive information about financial assets to investigate whether there are differences in the ownership and portfolio share of three asset classes among individuals who exhibit no mental account, a single mental account and multiple mental accounts, and the conditional influences of financial advice, housing, cognitive ability, time preference and risk tolerance. Overall I find that mental accounting together with financial advice and housing tenure explain variations in both the probability of ownership and portfolio share in the three asset classes. Households that exhibit a single mental account have low share of investments in, and are less likely to own, a risky asset when compared to those that exhibit no mental account or exhibit multiple mental accounts. I also find that, when compared to having no mental account, exhibiting a single mental account or multiple mental accounts increases both the probability and investment share in a fairly safe asset but decreases portfolio share in safe assets. In addition, among those that exhibit a single mental or multiple mental accounts, financial advice decreases portfolio share in risky assets and fairly safe assets and increases portfolio share in safe assets. Housing tenure increases both the probability and portfolio share in risky assets, decreases portfolio share in fairly safe assets and increases portfolio share in safe assets. These results are consistent using multi-equation regressions, sub-samples, reparametrised variables and poisson regressions. Finally, as little is known about how households derive the self-reported house prices estimates that are commonly used to determine housing wealth, the third study examines whether households are anchored on published house price indices. The key conjecture is that, while assessing the values of their homes, homeowners place more weight on house price news at the expense of property characteristics and other market information. I find support for this hypothesis using sixteen waves of the BHPS, multiple methods, and both regional and national house price indices. I conclude that changes in self-reported housing wealth are anchored on changes in published house price indices. Specifically, ownership through a mortgage and greater financial expectations increase anchoring effects while mortgage refinancing decreases the effects. Moreover, use of money raised from refinancing for home investment, as opposed to other consumption purposes, has a positive association with change in self-reported house value and both uses reduce anchoring bias. In addition, I find that computer use increases anchoring bias and, among social engagement mechanisms, religiosity reduces anchoring while other measures have no effect. These results are robust to internal instrumental variables, national aggregate house prices, alternative indices and sub-samples.