Related papers: Converting the reset
Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first…
We present a unified approach to those observables of stochastic processes under reset that take the form of averages of functionals depending on the most recent renewal period. We derive solutions for the observables, and determine the…
We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is…
Given a random time, we characterize the set of martingales for which the stopping theorems still hold. We also investigate how the stopping theorems are modified when we consider arbitrary random times. To this end, we introduce some…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
Predictive models are often used for real-time decision making. However, typical machine learning techniques ignore feature evaluation cost, and focus solely on the accuracy of the machine learning models obtained utilizing all the features…
We study the counting of level crossings for inertial random processes exposed to stochastic resetting events. We develop the general approach of stochastic resetting for inertial processes with sudden changes in the state characterized by…
Time series forecasting is important across various domains for decision-making. In particular, financial time series such as stock prices can be hard to predict as it is difficult to model short-term and long-term temporal dependencies…
A growing body of research has demonstrated that the behavior of large language models can be effectively controlled at inference time by directly modifying their internal states, either through vector additions to their activations or…
Time-series experiments, also called switchback experiments or N-of-1 trials, play increasingly important roles in modern applications in medical and industrial areas. Under the potential outcomes framework, recent research has studied…
I present the technique which can analyse some interest rate models: Constantinides-Ingersoll, CIR-model, geometric CIR and Geometric Brownian Motion. All these models have the unified structure of Whittaker function. The main focus of this…
We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an…
We propose that predictability is a prerequisite for profitability on financial markets. We look at ways to measure predictability of price changes using information theoretic approach and employ them on all historical data available for…
Forecasting central bank policy decisions remains a persistent challenge for investors, financial institutions, and policymakers due to the wide-reaching impact of monetary actions. In particular, anticipating shifts in the U.S. federal…
Causal reversibility blends reversibility and causality for concurrent systems. It indicates that an action can be undone provided that all of its consequences have been undone already, thus making it possible to bring the system back to a…
We present a simple model that uses time series momentum in order to construct strategies that systematically outperform their benchmark. The simplicity of our model is elegant: We only require a benchmark time series and several related…
This paper investigates short-term behaviors of implied volatility of derivatives written on indexes in equity markets when the index processes are constructed by using a ranking procedure. Even in simple market settings where stock prices…
We study the effect of persistence of engagement on learning in a stochastic multi-armed bandit setting. In advertising and recommendation systems, repetition effect includes a wear-in period, where the user's propensity to reward the…
An efficient method to price bonds with optional sinking feature is presented. Such instruments equip their issuer with the option (but not the obligation) to redeem parts of the notional prior to maturity, therefore the future cash flows…
Time reversal invariance can be summarized as follows: no difference can be measured if a sequence of events is run forward or backward in time. Because price time series are dominated by a randomness that hides possible structures and…