We propose a machine learning-based methodology which makes use of ensemble methods with the aims (i) treating missing data in time series irregular observation times and detecting anomalies observed behavior; (ii) defining suitable models system dynamics. applied this to US wholesale electricity price that are characterized by data, high stochastic volatility, jumps pronounced spikes. For we p...

We present a closed form solution to the perpetual American double barrier call option problem in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial irregular optimal stopping problem to an integro-differential free-boundary problem and solving the latter by using continuous and smooth fit. The obtained...

In this paper consistency problems for multi-factor jump-diffusion models, where the jump parts follow multivariate point processes are examined. First the gap between jump-diffusion models and generalized HeathJarrow-Morton (HJM) models is bridged. By applying the drift condition for a generalized arbitrage-free HJM model, the consistency condition for jumpdiffusion models is derived. Then we ...

This paper treats the risk-averse optimal portfolio problem with consumption in continuous time for a stochastic-jump-volatility, jump-diffusion (SJVJD) model of the underlying risky asset and the volatility. The new developments are the use of the SJVJD model with logtruncated-double-exponential jump-amplitude distribution in returns and exponential jumpamplitude distribution in volatility for...

In this paper, we provide for the first time an automated, correct-by-construction, controller synthesis scheme for a class of infinite dimensional stochastic hybrid systems, namely, hybrid stochastic retarded systems. First, we construct finite dimensional abstractions approximately bisimilar to original infinite dimensional stochastic systems having some stability property, namely, incrementa...

The goal of this paper is to show that the jump-diffusion models are an essential and easy-to-learn tool for option pricing and risk management, and that they provide an adequate description of stock price fluctuations and market risks. We try to give an overview of the field without focusing on technical details. After introducing several widely used jump-diffusion models, we discuss Fourier t...

Abstract: During the past and this decade, a new generation of continuous-time financial models has been intensively investigated in a quest to incorporate the so-called stylized empirical features of asset prices like fat-tails, high kurtosis, volatility clustering, and leverage. Modeling driven by “memoryless homogeneous” jump processes (Lévy processes) constitutes one of the most plausible d...

Affine jump-diffusion (AJD) processes constitute a large and widely used class of continuoustime asset pricing models that balance tractability and flexibility in matching market data. The prices of e.g., bonds, options, and other assets in AJD models are given by extended pricing transforms that have an exponential-affine form; these transforms have been characterized in great generality by Du...