Related papers: Explicit Computations for a Filtering Problem with…
We propose a change detection method for the famous Cox--Ingersoll--Ross model. This model is widely used in financial mathematics and therefore detecting a change in its parameters is of crucial importance. We develop one- and two-sided…
We consider learning causal relationships under conditional moment restrictions. Unlike causal inference under unconditional moment restrictions, conditional moment restrictions pose serious challenges for causal inference, especially in…
In this paper a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with…
Given a stochastic structure with a filtration $\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\mathbb{F}$ adapted non decreasing processes is considered. The…
We consider structural credit modeling in the important special case where the log-leverage ratio of the firm is a time-changed Brownian motion (TCBM) with the time-change taken to be an independent increasing process. Following the…
The utility-based pricing of defaultable bonds in the case of stochastic intensity models of default risk is discussed. The Hamilton-Jacobi- Bellman (HJB) equations for the value functions is derived. A finite difference method is used to…
Counting processes often written $N=(N_t)_{t\in\mathbb{R}^+}$ are used in several applications of biostatistics, notably for the study of chronic diseases. In the case of respiratory illness it is natural to suppose that the count of the…
We study adaptive sensing of Cox point processes, a widely used model from spatial statistics. We introduce three tasks: maximization of captured events, search for the maximum of the intensity function and learning level sets of the…
Diffusion in a linear potential in the presence of position-dependent killing is used to mimic a default process. Different assumptions regarding transport coefficients, initial conditions, and elasticity of the killing measure lead to…
We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The model assumes that all intensities share a common baseline intensity, which may for example represent the global market activity. Parameters…
This paper considers maximum likelihood inference for a functional marked point process - the stochastic growth-interaction process - which is an extension of the spatio-temporal growth-interaction process to the stochastic mark setting. As…
We present the method of moments approach to pricing barrier-type options when the underlying is modelled by a general class of jump diffusions. By general principles the option prices are linked to certain infinite dimensional linear…
We consider the forward investment problem in market models where the stock prices are continuous semimartingales adapted to a Brownian filtration. We construct a broad class of forward performance processes with initial conditions of power…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially-observed problem is reformulated into one with full observations, via a change of…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…
The two main approaches in credit risk are the structural approach pioneered in Merton (1974) and the reduced-form framework proposed in Jarrow & Turnbull (1995) and in Artzner & Delbaen (1995). The goal of this article is to provide a…
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…
The first passage time (FPT) problem is ubiquitous in many applications. In finance, we often have to deal with stochastic processes with jump-diffusion, so that the FTP problem is reducible to a stochastic differential equation with…
We build a general model for pricing defaultable claims. In addition to the usual absence of arbitrage assumption, we assume that one defaultable asset (at least) looses value when the default occurs. We prove that under this assumption, in…