We consider closed-form expansions for European put option prices within several stochastic volatility frameworks with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing a second-order Taylor expansion around the mean of its argument. The difficulties then faced are computing a number of expectations induced by the Taylor expansion in a closed-form manner. We establish a fast calibration scheme under the assumption that the parameters are piecewise-constant. Furthermore, we perform a sensitivity analysis to investigate the quality of our approximation and show that the errors are well within the acceptable range for application purposes. Lastly, we derive bounds on the remainder term due to the Taylor expansion.

We show that competitive equilibria in a range of useful production chain models can be recovered as the solutions to a class of dynamic programming problems. Bringing dynamic programming to bear on the equilibrium structure of production chains adds analytical power and opens new avenues for computation. In addition, the dynamic programming problem that we use to explore production chains is of interest in its own right, since it provides new optimality results for intertemporal choice in an empirically relevant setting.

Meeting the defined greenhouse gas (GHG) reduction targets in Germany is only possible by switching to renewable technologies in the energy sector. A major share of that reduction needs to be covered by the heat sector, which accounts for ~35% of the energy based emissions in Germany. Biomass is the renewable key player in the heterogeneous heat sector today. Its properties such as weather independency, simple storage and flexible utilization open up a wide field of applications for biomass. However, in a future heat sector fulfilling GHG reduction targets and energy sectors being increasingly connected: which bioenergy technology concepts are competitive options against other renewable heating systems? In this paper, the cost optimal allocation of the limited German biomass potential is investigated under longterm scenarios using a mathematical optimization approach. The model results show that bioenergy can be a competitive option in the future. Especially the use of biomass from residues can be highly competitive in hybrid combined heat and power (CHP) pellet combustion plants in the private household sector. However, towards 2050, wood based biomass use in high temperature industry applications is found to be the most cost efficient way to reduce heat based emissions by 95% in 2050.

A number of macroeconomic theories, very popular in the 1980s, seem to have completely disappeared and been replaced by the dynamic stochastic general equilibrium (DSGE) approach. We will argue that this replacement is due to a tacit agreement on a number of assumptions, previously seen as mutually exclusive, and not due to a settlement by 'nature'. As opposed to econometrics and microeconomics and despite massive progress in the access to data and the use of statistical software, macroeconomic theory appears not to be a cumulative science so far. Observational equivalence of different models and the problem of identification of parameters of the models persist as will be highlighted by examining two examples: one in growth theory and a second in testing inflation persistence.

With the increasing power of computers and the rapid development of self-learning methodologies such as machine learning and artificial intelligence, the problem of constructing an automatic Financial Trading Systems (FTFs) becomes an increasingly attractive research topic. An intuitive way of developing such a trading algorithm is to use Reinforcement Learning (RL) algorithms, which does not require model-building. In this paper, we dive into the RL algorithms and illustrate the definitions of the reward function, actions and policy functions in details, as well as introducing algorithms that could be applied to FTFs.