In my thesis I will be proposing situationalism: a new theory of how it is that things change over time. It is B-theoretic, eternalist and endurantist. The central contention of the theory is that what is true can differ in a metaphysically significant way from time to time. The theory emerges as a solution to the problem of change. In my first chapter, I argue that change is genuinely problematic (contra some of the recent literature). There are at least three ways to generate problems from change, and I elucidate problems from the law of non-contradiction and the indiscernibility of identicals. In the second chapter, I examine the nature of change and contend that the current major solutions to the problem fail to uphold our intuitive notion of change. Chapter 3 introduces the idea of a situation; a part of reality. The fourth chapter applies situations to the problem of change and comes up with a new solution. The solution relies on a denial of universal persistence; the denial of the idea that what is true in a situation s is thereby true in every situation of which s is a part. Chapter 5 considers the infamous Ship of Theseus case, and concludes that situationalism can also solve this problem. The situationalist account of the Ship of Theseus puzzle enables us, in Chapter 6, to briefly demonstrate the analogous application of the solution to a series of other persistence puzzles. The seventh chapter discusses the metaphysical consequences of such a view. The core claim is of the primacy of parts of reality over reality as a whole. It is a position according to which truth in situations is fundamental and situations needn’t cohere. I hold that the theory has significant costs but also substantial benefits. For this reason it is worth serious consideration.

In this thesis I discuss the method of time-change and its applications in quantitative finance. I mainly consider the time change by writing a continuous diffusion process as a Brownian motion subordinated by a subordinator process. I divide the time change method into two cases: deterministic time change and stochastic time change. The difference lies in whether the subordinator process is a deterministic function of time or a stochastic process of time. Time-changed Brownian motion with deterministic time change provides a new viewpoint to deal with option pricing under stochastic interest rates and I utilize this idea in pricing various exotic options under stochastic interest rates. Time-changed Brownian motion with stochastic time change is more complicated and I give the equivalence in law relation governing the ``original time" and the ``new stochastic time" under different clocks. This is readily applicable in pricing a new product called ``timer option". It can also be used in pricing barrier options under the Heston stochastic volatility model. Conclusion and further research directions in exploring the ideas of time change method in other areas of quantitative finance are in the last chapter.

In this thesis I discuss the method of time-change and its applications in quantitative finance. I mainly consider the time change by writing a continuous diffusion process as a Brownian motion subordinated by a subordinator process. I divide the time change method into two cases: deterministic time change and stochastic time change. The difference lies in whether the subordinator process is a deterministic function of time or a stochastic process of time. Time-changed Brownian motion with deterministic time change provides a new viewpoint to deal with option pricing under stochastic interest rates and I utilize this idea in pricing various exotic options under stochastic interest rates. Time-changed Brownian motion with stochastic time change is more complicated and I give the equivalence in law relation governing the ``original time" and the ``new stochastic time" under different clocks. This is readily applicable in pricing a new product called ``timer option". It can also be used in pricing barrier options under the Heston stochastic volatility model. Conclusion and further research directions in exploring the ideas of time change method in other areas of quantitative finance are in the last chapter.

This dissertation collects two papers regarding the econometric and economic theory and testing of the predictability of asset returns. It is widely accepted that stock returns are not only predictable but highly so. This belief is due to an abundance of existing empirical literature fi nding often overwhelming evidence in favor of predictability. The common regressors used to test predictability (e.g., the dividend-price ratio for stock returns) are very persistent and their innovations are highly correlated with returns. Persistence when combined with a correlation between innovations in the regressor and asset returns can cause substantial over-rejection of a true null hypothesis. This result is both well documented and well known. On the other hand, stochastic volatility is both broadly accepted as a part of return time series and largely ignored by the existing econometric literature on the predictability of returns. The severe e ffect that stochastic volatility can have on standard tests are demonstrated here. These deleterious e ffects render standard tests invalid. However, this problem can be easily corrected using a simple change of chronometer. When a return time series is read in the usual way, at regular intervals of time (e.g., daily observations), then the distribution of returns is highly non-normal and displays marked time heterogeneity. If the return time series is, instead, read according to a clock based on regular intervals of volatility, then returns will be independent and identically normally distributed. This powerful result is utilized in a unique way in each chapter of this dissertation. This time-deformation technique is combined with the Cauchy t-test and the newly introduced martingale estimation technique. This dissertation nds no evidence of predictability in stock returns. Moreover, using martingale estimation, the cause of the Forward Premium Anomaly may be more easily discerned.

<p>The central theme of this thesis is to develop methods of financial mathematics to understand the dynamics of a firm's capital structure through observations of market prices of liquid securities written on the firm. Just as stock prices are a direct measure of a firm's equity, other liquidly traded products such as options and credit default swaps (CDS) should also be indicators of aspects of a firm's capital structure. We interpret the prices of these securities as the market's revelation of a firm's financial status. In order not to enter into the complexity of balance sheet anatomy, we postulate a balance sheet as simple as Asset = Equity + Debt. Using mathematical models based on the principles of arbitrage pricing theory, we demonstrate that this reduced picture is rich enough to reproduce CDS term structures and implied volatility surfaces that are consistent with market observations. Therefore, reverse engineering applied to market observations provides concise and crucial information of the capital structure.</p> <p>Our investigations into capital structure modeling gives rise to an innovative pricing formula for spread options. Existing methods of pricing spread options are not entirely satisfactory beyond the log-normal model and we introduce a new formula for general spread option pricing based on Fourier analysis of the payoff function. Our development, including a flexible and general error analysis, proves the effectiveness of a fast Fourier transform implementation of the formula for the computation of spread option prices and Greeks. It is found to be easy to implement, stable, and applicable in a wide variety of asset pricing models.</p> / Doctor of Philosophy (PhD)

Currently, there is a legislative procedure in the EU to abolish switching of time regimes. Under this procedure, member countries should choose to observe either permanent Standard Time (ST) or permanent Daylight Saving Time (DST). We study whether the time regime has an effect on how people spend their time. The data we are using are daily time use panel data of US citizens from the American Time Use Survey from 2003 to 2019. To study time use of daily activities, we combine the short-run before-after effect of time regime switch with the long-run comparison of time regimes in Difference-in-Differences. We layout basic implications for EU member states, regarding individuals' time use preferences, and the time regime reform.

<p>Brownian motion has met growing interest in mathematics, physics and particularly in finance since it was introduced in the beginning of the twentieth century. Stochastic processes generalizing Brownian motion have influenced many research fields theoretically and practically. Moreover, along with more refined techniques in measure theory and functional analysis more stochastic processes were constructed and studied. Lévy processes, with Brownian motionas a special case, have been of major interest in the recent decades. In addition, Lévy processes include a number of other important processes as special cases like Poisson processes and subordinators. They are also related to stable processes.</p><p>In this thesis we generalize a result by S. Chandrasekhar [2] and Edward Nelson who gave a detailed proof of this result in his book in 1967 [12]. In Nelson’s first result standard Ornstein-Uhlenbeck processes are studied. Physically this describes free particles performing a random and irregular movement in water caused by collisions with the water molecules. In a further step he introduces a nonlinear drift in the position variable, i.e. he studies the case when these particles are exposed to an external field of force in physical terms.</p><p>In this report, we aim to generalize the result of Edward Nelson to the case of α-stable Lévy processes. In other words we replace the driving noise of a standard Ornstein-Uhlenbeck process by an α-stable Lévy noise and introduce a scaling parameter uniformly in front of all vector fields in the cotangent space, even in front of the noise. This corresponds to time being sent to infinity. With Chandrasekhar’s and Nelson’s choice of the diffusion constant the stationary state of the velocity process (which is approached as time tends to infinity) is the Boltzmann distribution of statistical mechanics.The scaling limits we obtain in the absence and presence of a nonlinear drift term by using the scaling property of the characteristic functions and time change, can be extended to other types of processes rather than α-stable Lévy processes.</p><p>In future, we will consider to generalize this one dimensional result to Euclidean space of arbitrary finite dimension. A challenging task is to consider the geodesic flow on the cotangent bundle of a Riemannian manifold with scaled drift and scaled Lévy noise. Geometrically the Ornstein-Uhlenbeck process is defined on the tangent bundle of the real line and the driving Lévy noise is defined on the cotangent space.</p>

This theoretic-empiric thesis concerns the transformation of parent's leisure time taking parental leave, analyzes the leisure time of parents who decided to stay at home with children. Thesis focuses on factors most affecting the leisure time and primarily look on effect coming from change of social role itself. Additionally brings research of parent's leisure activities and the effect of change of leisure behavior on other areas of family life during the parental leave. Research tries to expose signification of the leisure time in this critical family time period as well as effect on parents through the parental leave. The theoretical base was created with collecting sources concerning leisure time area, social role change, parental leave and its application on particular field of leisure time change. Results of thesis coming from qualitative research based on qualitative analysis of a couple deeper dialogs moderated according to research strategy - methods anchored theory and application on contemporary knowledge.

Brownian motion has met growing interest in mathematics, physics and particularly in finance since it was introduced in the beginning of the twentieth century. Stochastic processes generalizing Brownian motion have influenced many research fields theoretically and practically. Moreover, along with more refined techniques in measure theory and functional analysis more stochastic processes were constructed and studied. Lévy processes, with Brownian motionas a special case, have been of major interest in the recent decades. In addition, Lévy processes include a number of other important processes as special cases like Poisson processes and subordinators. They are also related to stable processes. In this thesis we generalize a result by S. Chandrasekhar [2] and Edward Nelson who gave a detailed proof of this result in his book in 1967 [12]. In Nelson’s first result standard Ornstein-Uhlenbeck processes are studied. Physically this describes free particles performing a random and irregular movement in water caused by collisions with the water molecules. In a further step he introduces a nonlinear drift in the position variable, i.e. he studies the case when these particles are exposed to an external field of force in physical terms. In this report, we aim to generalize the result of Edward Nelson to the case of α-stable Lévy processes. In other words we replace the driving noise of a standard Ornstein-Uhlenbeck process by an α-stable Lévy noise and introduce a scaling parameter uniformly in front of all vector fields in the cotangent space, even in front of the noise. This corresponds to time being sent to infinity. With Chandrasekhar’s and Nelson’s choice of the diffusion constant the stationary state of the velocity process (which is approached as time tends to infinity) is the Boltzmann distribution of statistical mechanics.The scaling limits we obtain in the absence and presence of a nonlinear drift term by using the scaling property of the characteristic functions and time change, can be extended to other types of processes rather than α-stable Lévy processes. In future, we will consider to generalize this one dimensional result to Euclidean space of arbitrary finite dimension. A challenging task is to consider the geodesic flow on the cotangent bundle of a Riemannian manifold with scaled drift and scaled Lévy noise. Geometrically the Ornstein-Uhlenbeck process is defined on the tangent bundle of the real line and the driving Lévy noise is defined on the cotangent space.

I consider continuous time asset pricing models with stochastic differential utility incorporating decision makers' concern with ambiguity on true probability measure. In order to identify and estimate key parameters in the models, I use a novel econometric methodology developed recently by Park (2008) for the statistical inference on continuous time conditional mean models. The methodology only imposes the condition that the pricing error is a continuous martingale to achieve identification, and obtain consistent and asymptotically normal estimates of the unknown parameters. Under a representative agent setting, I empirically evaluate alternative preference specifications including a multiple-prior recursive utility. My empirical findings are summarized as follows: Relative risk aversion is estimated around 1.5-5.5 with ambiguity aversion and 6-14 without ambiguity aversion. Related, the estimated ambiguity aversion is both economically and statistically significant and including the ambiguity aversion clearly lowers relative risk aversion. The elasticity of intertemporal substitution (EIS) is higher than 1, around 1.3-22 with ambiguity aversion, and quite high without ambiguity aversion. The identification of EIS appears to be fairly weak, as observed by many previous authors, though other aspects of my empirical results seem quite robust. Next, I develop an approach to test for martingale in a continuous time framework. The approach yields various test statistics that are consistent against a wide class of nonmartingale semimartingales. A novel aspect of my approach is to use a time change defined by the inverse of the quadratic variation of a semimartingale, which is to be tested for the martingale hypothesis. With the time change, a continuous semimartingale reduces to Brownian motion if and only if it is a continuous martingale. This follows immediately from the celebrated theorem by Dambis, Dubins and Schwarz. For the test of martingale, I may therefore see if the given process becomes Brownian motion after the time change. I use several existing tests for multivariate normality to test whether the time changed process is indeed Brownian motion. I provide asymptotic theories for my test statistics, on the assumption that the sampling interval decreases, as well as the time horizon expands. The stationarity of the underlying process is not assumed, so that my results are applicable also to nonstationary processes. A Monte-Carlo study shows that our tests perform very well for a wide range of realistic alternatives and have superior power than other discrete time tests.