Related papers: Representation for martingales living after a rand…
We derive the asymptotic first passage time (FPT) distribution for space-dependent variable-order time-fractional diffusion, where the fractional exponent $\alpha(x)$ varies with position. For any sufficiently smooth $\alpha(x)$ on a finite…
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…
In this article, we provide different representations for a time-fractional birth and death process $N_{\alpha}(t)$, whose transition probabilities are governed by a time-fractional system of differential equations. More specifically, we…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
The long-term behavior of a supercritical branching random walk can be described and analyzed with the help of Biggins' martingales, parametrized by real or complex numbers. The study of these martingales with complex parameters is a rather…
This paper completes the two studies undertaken in \cite{aksamit/choulli/deng/jeanblanc2} and \cite{aksamit/choulli/deng/jeanblanc3}, where the authors quantify the impact of a random time on the No-Unbounded-Risk-with-Bounded-Profit…
In this paper, we aim at characterizing generalized functionals of discrete-time normal martingales. Let $M=(M_n)_{n\in \mathbb{N}}$ be a discrete-time normal martingale that has the chaotic representation property. We first construct…
In this article, we consider time-changed models of population evolution $\mathcal{X}^f(t)=\mathcal{X}(H^f(t))$, where $\mathcal{X}$ is a counting process and $H^f$ is a subordinator with Laplace exponent $f$. In the case $\mathcal{X}$ is a…
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…
We propose a new approach to utilities that is consistent with state-dependent utilities. In our model utilities reflect the level of consumption satisfaction of flows of cash in future times as they are valued when the economic agents are…
Considered a pair of random lifetimes whose dependence is described by a Time Transformed Exponential model, we provide analytical expressions for the distribution of their sum. These expressions are obtained by using a representation of…
In settings ranging from weather forecasts to political prognostications to financial projections, probability estimates of future binary outcomes often evolve over time. For example, the estimated likelihood of rain on a specific day…
In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these…
We start with a general governing equation for diffusion transport, written in a conserved form, in which the phenomenological flux laws can be constructed in a number of alternative ways. We pay particular attention to flux laws that can…
In this article, a sensitivity analysis of long-term cash flows with respect to perturbations in the underlying process is presented. For this purpose, we employ the martingale extraction through which a pricing operator is transformed into…
In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations,…
Lions and Musiela (2007) give sufficient conditions to verify when a stochastic exponential of a continuous local martingale is a martingale or a uniformly integrable martingale. Blei and Engelbert (2009) and Mijatovi\'c and Urusov (2012c)…
We define and study the $T\bar{T}$ deformation of a random matrix model, showing a consistent definition requires the inclusion of both the perturbative and non-perturbative solutions to the flow equation. The deformed model is well defined…
We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…
In this paper we show that the weak representation property of a semimartingale $X$ with respect to a filtration $\mathbb{F}$ is preserved in the progressive enlargement $\mathbb{G}$ by a random time $\tau$ avoiding $\mathbb{F}$-stopping…