Related papers: On the martingale property in stochastic volatilit…

A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general…

We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…

This dissertation investigates the ability of the Ising model to replicate statistical characteristics, or stylized facts, commonly observed in financial assets. The study specifically examines in the S&P500 index the following features:…

The distribution of price returns for a class of uncorrelated diffusive dynamics is considered. The basic assumptions are (1) that there is a "consensus" value associated with a stock, and (2) that the rate of diffusion depends on the…

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random…

We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving…

Positive $T$-martingales were developed as a general framework that extends the positive measure-valued martingales and are meant to model intermittent turbulence. We extend their scope by allowing the martingale to take complex values. We…

We introduce a multivariate stochastic volatility model for asset returns that imposes no restrictions to the structure of the volatility matrix and treats all its elements as functions of latent stochastic processes. When the number of…

Causal reasoning has gained great attention over the last half century as it allows (or at least intends) to answer questions which go above those within the capabilities of classical inferential statistics using just observational data. So…

We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…

Comparison results are given for time-inhomogeneous Markov processes with respect to function classes induced stochastic orderings. The main result states comparison of two processes, provided that the comparability of their infinitesimal…

We establish a general analytic framework for determining the AF-martingale dimension of diffusion processes associated with strongly local regular Dirichlet forms on metric measure spaces. While previous approaches typically relied on…

Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to…

In this paper we look at the properties of limits of a sequence of real valued time inhomogeneous diffusions. When convergence is only in the sense of finite-dimensional distributions then the limit does not have to be a diffusion. However,…

In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…

It is known since Kellerer (1972) that for any process that is increasing for the convex order, or "peacock" as in Hirsch et al. 2011, there exist martingales with the same marginals laws. Nevertheless, there is no general constructive…

No-arbitrage asset pricing characterizes valuation through the existence of equivalent martingale measures relative to a filtration and a class of admissible trading strategies. In practice, pricing is performed across multiple asset…

We introduce the concept of stochastic measure-valued solutions to the complete Euler system describing the motion of a compressible inviscid fluid subject to stochastic forcing, where the nonlinear terms are described by defect measures.…

We refine stochastic calculus for symmetric Markov processes without using time reverse operators. Under some conditions on the jump functions of locally square integrable martingale additive functionals, we extend Nakao's divergence-like…

For a class of symmetric random matrices whose entries are martingale differences adapted to an increasing filtration, we prove that under a Lindeberg-like condition, the empirical spectral distribution behaves asymptotically similarly to a…