An optimal prediction problem in financial modelling
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A constrained informationally efficient market is defined as one in which the price process arises as the outcome of some equilibrium where agents face restrictions on trade. This paper investigates the case of short sale constraints, a setting which, desp ...
I started my Ph.D. studies in the Fall 2008, a period ex-post perceived as being at the core of the Financial Crisis. At that time my ideas were vague and I struggled to find a good research topic. As surprising as it might appear, in one single week the d ...
We investigate a stochastic signal-processing framework for signals with sparse derivatives, where the samples of a Levy process are corrupted by noise. The proposed signal model covers the well-known Brownian motion and piecewise-constant Poisson process; ...
We study stationary max-stable processes {n(t): t is an element of R} admitting a representation of the form n(t) = max(i is an element of N) (U-i +Y-i(t)), where Sigma(infinity)(i=1) delta U-i is a Poisson point process on R with intensity e(-u)du, and Y1 ...
This paper is devoted to the characterization of an extended family of continuous-time autoregressive moving average (CARMA) processes that are solutions of stochastic differential equations driven by white Levy innovations. These are completely specified ...
We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by some generalized ...
Investors' inheterogeneity is one of the prevailing features on financial markets. Thus, the recent asset pricing literature has produced a number of general equilibrium models where agents have different preferences. This thesis analyzes the effect of pre ...
The aim of this note is to show that the classical results in finance theory for pricing of derivatives, given by making use of the replication principle, can be extended to the noncommutative world. We believe that this could be of interest in quantum pro ...
We introduce in this thesis the idea of a variable lookback model, i.e., a model whose predictions are based on a variable portion of the information set. We verify the intuition of this model in the context of experimental finance. We also propose a novel ...
When a strict local martingale is projected onto a subfiltration to which it is not adapted, the local martingale property may be lost, and the finite variation part of the projection may have singular paths. This phenomenon has consequences for arbitrage ...
