Related papers: Alpha-CIR Model with Branching Processes in Sovere…

In this paper, we consider three stochastic-volatility models, each characterized by distinct dynamics of instantaneous volatility: (1) a CIR process for squared volatility (i.e., the classical Heston model); (2) a mean-reverting lognormal…

Motivated by machine learning, we introduce a novel method for randomly generating inflationary potentials. Namely, we treat the Taylor coefficients of the potential as weights in a single-layer neural network and use gradient ascent to…

We consider a branching stable process with positive jumps, i.e. a continuous-time branching process in which the particles evolve independently as stable L{\'e}vy processes with positive jumps. Assuming the branching mechanism is critical…

This paper provides a discrete time LIBOR analog, which can be used for arbitrage-free discretization of Levy LIBOR models or discrete approximation of continuous time LIBOR market models. Using the work of Eberlein and Oezkan as an…

We develop a multi-factor stochastic volatility Libor model with displacement, where each individual forward Libor is driven by its own square-root stochastic volatility process. The main advantage of this approach is that, maturity-wise,…

In this paper, we consider the Heston-CIR model with L\'{e}vy process for pricing in the foreign exchange (FX) market by providing a new formula that better fits the distribution of prices. To do that, first, we study the existence and…

In our model, private actors with interbank cash flows similar to, but nore general than (Carmona, Fouque, Sun, 2013) borrow from the outside economy at a certain interest rate, controlled by the central bank, and invest in risky assets.…

We study extensions of the classical SIR model of epidemic spread. First, we consider a single population modified SIR epidemics model in which the contact rate is allowed to be an arbitrary function of the fraction of susceptible and…

We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under…

In this paper, we present an alternative perspective on the mean-field LIBOR market model introduced by Desmettre et al. in arXiv:2109.10779. Our novel approach embeds the mean-field model in a classical setup, but retains the crucial…

At present, there is an explosion of practical interest in the pricing of interest rate (IR) derivatives. Textbook pricing methods do not take into account the leptokurticity of the underlying IR process. In this paper, such a leptokurtic…

Traditional studies about disease dynamics have focused on global stability issues, due to their epidemiological importance. We study a classical SIR-SI model for arboviruses in two different directions: we begin by describing an…

In this paper we present the discrete-time networked SIR and SEIR models and present assumptions under which they are well defined. We analyze the limiting behavior of the models and present necessary and sufficient conditions for…

This paper explores a comprehensive class of time-changed stochastic processes constructed by subordinating Brownian motion with Levy processes, where the subordination is further governed by stochastic arrival mechanisms such as the Cox…

In this letter, I consider the issue of pricing risky debt by following Merton's approach. I generalize Merton's results to the case where the interest rate is modeled by the CIR term structure. Exact closed forms are provided for the risky…

The shapes of branching trees have been linked to disease transmission patterns. In this paper we use the general Crump-Mode-Jagers branching process to model an outbreak of an infectious disease under mild assumptions. Introducing a new…

The hypothesis that committed revolving credit lines with fixed spreads can provide firms with interest rate insurance is a standard feature of models on these credit facilities' interest rate structure. Nevertheless, this hypothesis has…

We summarize our work on constant roll inflationary models. It was understood recently that constant roll inflation, in a regime beyond the slow roll approximation, can give models that are in agreement with the observational constraints.…

We introduce and study the class of branching-stable point measures, which can be seen as an analog of stable random variables when the branching mechanism for point measures replaces the usual addition. In contrast with the classical…

Pure-jump L\'evy processes are popular classes of stochastic processes which have found many applications in finance, statistics or machine learning. In this paper, we propose a novel family of self-decomposable L\'evy processes where one…