Related papers: Maximum likelihood approach for several stochastic…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…
This survey reviews portfolio choice in settings where investment opportunities are stochastic due to, e.g., stochastic volatility or return predictability. It is explained how to heuristically compute candidate optimal portfolios using…
We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…
When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task…
We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is…
Recently Carr and Wu (2004, 2005) and also Huang and Wu (2004) show that most stochastic processes used in traditional option pricing models can be cast as special cases of time-changed L\'evy processes. In particular these are models which…
Volatility is a natural risk measure in finance as it quantifies the variation of stock prices. A frequently considered problem in mathematical finance is to forecast different estimates of volatility. What makes it promising to use deep…
We consider the robust utility maximization using a static holding in derivatives and a dynamic holding in the stock. There is no fixed model for the price of the stock but we consider a set of probability measures (models) which are not…
Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of…
We prove the strong consistency and the asymptotic normality of the maximum likelihood estimator of the parameters of a general conditionally heteroscedastic model with $\alpha$-stable innovations. Then, we relax the assumptions and only…
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit…
We consider a mean-reverting stochastic volatility model which satisfies some relevant stylized facts of financial markets. We introduce an algorithm for the detection of peaks in the volatility profile, that we apply to the time series of…
We consider the short time behaviour of stochastic systems affected by a stochastic volatility evolving at a faster time scale. We study the asymptotics of a logarithmic functional of the process by methods of the theory of homogenisation…
Recent empirical evidence has highlighted the crucial role of jumps in both price and volatility within the cryptocurrency market. In this paper, we integrate price--volatility co-jumps and volatility short-term dependency into a coherent…
The development of new methods and representations for temporal decision-making requires a principled basis for characterizing and measuring the flexibility of decision strategies in the face of uncertainty. Our goal in this paper is to…
A novel approach called Moate Simulation is presented to provide an accurate numerical evolution of probability distribution functions represented on grids arising from stochastic differential processes where initial conditions are…
The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models…
Parametric estimation of stochastic differential equations (SDEs) has been a subject of intense studies already for several decades. The Heston model for instance is driven by two coupled SDEs and is often used in financial mathematics for…
Recent years have seen an increased level of interest in pricing equity options under a stochastic volatility model such as the Heston model. Often, simulating a Heston model is difficult, as a standard finite difference scheme may lead to…