Related papers: Long Run Law and Entropy
This paper studies the long-term growth rate of expected utility from holding a leveraged exchanged-traded fund (LETF), which is a constant proportion portfolio of the reference asset. Working with the power utility function, we develop an…
An influential theory of increasing returns has been proposed by the economist W. B. Arthur in the '80s to explain the lock-in phenomenon between two competing commercial products. In the most simplified situation there are two competing…
In this paper we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale…
The specific relative entropy, introduced by N. Gantert, allows to quantify the discrepancy between the laws of potentially mutually singular measures. It appears naturally as the large deviations rate function in a randomized version of…
Let $(\xi_1, \eta_1)$, $(\xi_2, \eta_2),\ldots$ be independent identically distributed $\mathbb{R}^2$-valued random vectors. We prove a strong law of large numbers, a functional central limit theorem and a law of the iterated logarithm for…
We present a novel approach for predicting the distribution of asset returns using a quantile-based method with Long Short-Term Memory (LSTM) networks. Our model is designed in two stages: the first focuses on predicting the quantiles of…
We establish functional limit theorems for ergodic sums of observables with power singularities for expanding circle maps. In the regime where the observables have infinite variance, we show that when rescaled by $N^{1/s}(\ln N)^\alpha$,…
The dynamics of nonlinear conservation laws have long posed fascinating problems. With the introduction of some nonlinearity, e.g. Burgers' equation, discontinuous behavior in the solutions is exhibited, even for smooth initial data. The…
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 analyze almost sure asymptotic behavior of extreme values of a regenerative process. We show that under certain conditions a properly centered and normalized running maximum of a regenerative process satisfies a law of the iterated…
In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a…
The information dynamics in finance and insurance applications is usually modeled by a filtration. This paper looks at situations where information restrictions apply such that the information dynamics may become non-monotone. A fundamental…
We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…
The classical Merton investment problem predicts deterministic, state-dependent portfolio rules; however, laboratory and field evidence suggests that individuals often prefer randomized decisions leading to stochastic and noisy choices.…
Scale invariance, collective behaviours and structural reorganization are crucial for portfolio management (portfolio composition, hedging, alternative definition of risk, etc.). This lack of any characteristic scale and such elaborated…
A complete characterization of the possible joint distributions of the maximum and terminal value of uniformly integrable martingale has been known for some time, and the aim of this paper is to establish a similar characterization for…
The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in…
Models to price long term loans in the securities lending business are developed. These longer horizon deals can be viewed as contracts with optionality embedded in them. This insight leads to the usage of established methods from…
We study the market selection hypothesis in complete financial markets, populated by heterogeneous agents. We allow for a rich structure of heterogeneity: individuals may differ in their beliefs concerning the economy, information and…