Finance Without Brownian Motions: An Introduction To Simplified Stochastic Calculus

The paper introduces a simple way of recording and manipulating stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no jumps are physically present). The new calculus is thus intuitive and compact. The calculus is also fail-safe in that, under minimal assumptions, all formal calculations are guaranteed to yield mathematically well-defined stochastic processes. Several illustrative examples of the new concept are given, among them a novel result on the Margrabe option to exchange one defaultable asset for another

The Complexity of Finding Reset Words in Finite Automata

We study several problems related to finding reset words in deterministic finite automata. In particular, we establish that the problem of deciding whether a shortest reset word has length k is complete for the complexity class DP. This result answers a question posed by Volkov. For the search problems of finding a shortest reset word and the length of a shortest reset word, we establish membership in the complexity classes FP^NP and FP^NP[log], respectively. Moreover, we show that both these problems are hard for FP^NP[log]. Finally, we observe that computing a reset word of a given length is FNP-complete.Comment: 16 pages, revised versio

A counterexample concerning the variance-optimal martingalle measure

The present note addresses an open question concerning a sufficient characterization of the variance-optimal martingale measure

Thermal Conductivity of High Performance Concrete in Wide Temperature and Moisture Ranges

The thermal conductivity of two types of high performance concrete was measured in the temperature range from 100 °C to 800 °C and in the moisture range from dry material to saturation water content. A transient measuring method based on analysis of the measured temperature fields was chosen for the high temperature measurements, and a commercial hot wire device was employed in room temperature measurements of the effect of moisture on thermal conductivity. The measured results reveal that both temperature and moisture exhibit significant effects on the values of thermal conductivity, and these effects are quite comparable from the point of view of the magnitude of the observed variations

Thermal and Hygric Expansion of High Performance Concrete

The linear thermal expansion coefficient of two types of high performance concrete was measured in the temperature range from 20 °C to 1000 °C, and the linear hygric expansion coefficient was determined in the moisture range from dry material to saturation water content. Comparative methods were applied for measurements of both coefficients. The experimental results show that both the effect of temperature on the values of linear thermal expansion coefficients and the effect of moisture on the values of linear hygric expansion coefficients are very significant and cannot be neglected in practical applications

Temperature and Moisture Dependence of the Specific Heat of High Performance Concrete

The specific heat of two types of high performance concrete was measured in the temperature range from 20 °C to 1000 °C and in the moisture range from dry material to saturation water content. A nonadiabatic method was chosen instead of classical adiabatic treatments in order to meet the requirements following from the large representative elementary volume of the materials. The measured results reveal a significant temperature effect on the specific heat value. The influence of moisture is less important than the influence of temperature, but is also not negligible

Finitely generated ideal languages and synchronizing automata

We study representations of ideal languages by means of strongly connected synchronizing automata. For every finitely generated ideal language L we construct such an automaton with at most 2^n states, where n is the maximal length of words in L. Our constructions are based on the De Bruijn graph.Comment: Submitted to WORDS 201

Pure-jump semimartingales

A taxonomic hierarchy of pure-jump semimartingales is introduced. This hierarchy contains, in particular, the class of sigma-locally finite variation pure-jump processes. The members of this family can be explicitly characterized in terms of the predictable compensators of their jump measures. This family is also closed under stochastic integration and smooth transformations

Optimal Trade Execution Under Endogenous Pressure to Liquidate: Theory and Numerical Solutions

We study optimal liquidation of a trading position (so-called block order or meta-order) in a market with a linear temporary price impact (Kyle, 1985). We endogenize the pressure to liquidate by introducing a downward drift in the unaffected asset price while simultaneously ruling out short sales. In this setting the liquidation time horizon becomes a stopping time determined endogenously, as part of the optimal strategy. We find that the optimal liquidation strategy is consistent with the square-root law which states that the average price impact per share is proportional to the square root of the size of the meta-order (Bershova and Rakhlin, 2013; Farmer et al., 2013; Donier et al., 2015; T´oth et al., 2016). Mathematically, the Hamilton-Jacobi-Bellman equation of our optimization leads to a severely singular and numerically unstable ordinary differential equation initial value problem. We provide careful analysis of related singular mixed boundary value problems and devise a numerically stable computation strategy by re-introducing time dimension into an otherwise time-homogeneous task

Comparison of the Capacitance Method and the Microwave Impulse Method for Determination of Moisture Profiles in Building Materials

A comparison of the capacitance method and the microwave impulse method for the determination of moisture profiles in three typical porous building materials is presented in this paper. The basic principles of the measuring methods are given. The calibration process is described in detail. On the basis of the measured results, it can be concluded that the capacitance method provides better accuracy in the range of lower moisture content than to the microwave impulse method, which is more accurate for the highest values of moisture content.