Related papers: Long Run Law and Entropy
In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to power law distributions. For such a random walk, we study…
This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…
We analyse four consecutive cycles observed in the USA for employment and inflation. They are driven by three oil price shocks and an intended interest rate shock. Non-linear coupling between the rate equations for consumer products as prey…
In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix…
In this paper we study the distribution of hitting and return times for observations of dynamical systems. We apply this results to get an exponential law for the distribution of hitting and return times for rapidly mixing random dynamical…
We consider a continuous-time financial market with no arbitrage and no transactions costs. In this setting, we introduce two types of perpetual contracts, one in which the payoff to the long side is a fixed function of the underlyers and…
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…
Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile…
This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdisciplinary research area of extreme events, underlining its…
Using a model based on generalised Lotka Volterra dynamics together with some recent results for the solution of generalised Langevin equations, we show that the equilibrium solution for the probability distribution of wealth has two…
In an $L_\infty$-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems…
Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two…
This study presents contemporaneous modeling of asset return and price range within the framework of stochastic volatility with leverage. A new representation of the probability density function for the price range is provided, and its…
This review summarizes the historical development of probability measures in asset pricing, from early mathematical finance and state price theory to risk-neutral valuation, martingale measures, forward measures, stochastic discount…
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…
Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between…
Scaling Laws have emerged as a powerful framework for understanding how model performance evolves as they increase in size, providing valuable insights for optimizing computational resources. In the realm of Sequential Recommendation (SR),…
Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are…
We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution…
In this paper we propose a general derivative pricing framework which employs decoupled time-changed (DTC) L\'evy processes to model the underlying asset of contingent claims. A DTC L\'evy process is a generalized time-changed L\'evy…