Related papers: Long Run Law and Entropy
Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process with innovations in the domain of attraction of an $\alpha$-stable law $(0<\alpha<2)$. Assume that the linear process $X$ has a bounded probability density function $f(x)$.…
We consider the mean-variance hedging problem under partial information in the case where the flow of observable events does not contain the full information on the underlying asset price process. We introduce a martingale equation of a new…
Understanding the statistical properties of recurrence intervals of extreme events is crucial to risk assessment and management of complex systems. The probability distributions and correlations of recurrence intervals for many systems have…
This paper considers general term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We give a general model starting from families of forward rates driven by infinitely many Brownian motions and…
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small…
In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…
We study the martingale property and moment explosions of a signature volatility model, where the volatility process of the log-price is given by a linear form of the signature of a time-extended Brownian motion. Excluding trivial cases, we…
In this paper, we develop a general law of large numbers and central limit theorem for cumulative reward processes associated with finite state Markov jump processes with non-stationary transition rates. Such models commonly arise in…
Recommendations based on behavioral data may be faced with ambiguous statistical evidence. We consider the case of association rules, relevant e.g.~for query and product recommendations. For example: Suppose that a customer belongs to…
We discuss martingales, detrending data, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that Martingale stochastic…
We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with…
We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded…
In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…
Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter…
This paper develops a method to derive optimal portfolios and risk premia explicitly in a general diffusion model for an investor with power utility and a long horizon. The market has several risky assets and is potentially incomplete.…
We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra.…
An axiomatic approach to macroeconomics based on the mathematical structure of thermodynamics is presented. It deduces relations between aggregate properties of an economy, concerning quantities and flows of goods and money, prices and the…
Based on a martingale theory approach, we present a complete characterization of the asymptotic behaviour of a lazy reinforced random walk (LRRW) which shows three different regimes (diffusive, critical and superdiffusive). This allows us…
We introduce an additive stochastic mortality model which allows joint modelling and forecasting of underlying death causes. Parameter families for mortality trends can be chosen freely. As model settings become high dimensional, Markov…
Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the…