Related papers: A Basic Overview of Various Stochastic Approaches …
In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton-Jacobi-Bellman equation…
We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets. Both the asset value and the volatility processes are correlated through systemic Brownian motions, with default determined by…
One approach to the analysis of stochastic fluctuations in market prices is to model characteristics of investor behaviour and the complex interactions between market participants, with the aim of extracting consequences in the aggregate.…
We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure,…
Measuring model risk is required by regulators on financial and insurance markets. We separate model risk into parameter estimation risk and model specification risk, and we propose expected shortfall type model risk measures applied to…
The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…
This paper describes a general approach for stochastic modeling of assets returns and liability cash-flows of a typical pensions insurer. On the asset side, we model the investment returns on equities and various classes of fixed-income…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
One of the main tasks in the study of financial and economic processes is forecasting and analysis of the dynamics of these processes. Within this task lie important research questions including how to determine the qualitative properties…
Stochastic models of varying complexity have been proposed to describe the dispersion of particles in turbulent flows, from simple Brownian motion to complex temporally and spatially correlated models. A method is needed to compare…
In quantitative finance, modeling the volatility structure of underlying assets is vital to pricing options. Rough stochastic volatility models, such as the rough Bergomi model [Bayer, Friz, Gatheral, Quantitative Finance 16(6), 887-904,…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
In this paper, we introduce a suite of models for price-aware automated market making platforms willing to optimize their quotes. These models incorporate advanced price dynamics, including stochastic volatility, jumps, and microstructural…
Stochastic models with fractional Brownian motion as source of randomness have become popular since the early 2000s. Fractional Brownian motion (fBm) is a Gaussian process, whose covariance depends on the so-called Hurst parameter $H\in…
In this article we model a financial derivative price as an observable on the market state function. We apply geometric techniques to integrating the Heisenberg Equation of Motion. We illustrate how the non-commutative nature of the model…
New theoretical approaches about forecasting stock markets are proposed. A mathematization of the stock market in terms of arithmetical relations is given, where some simple (non-differential, non-fractal) expressions are also suggested as…
Since the introduction of Dyson's Brownian motion in early 1960's, there have been a lot of developments in the investigation of stochastic processes on the space of Hermitian matrices. Their properties, especially, the properties of their…
This paper presents a new prediction model for time series data by integrating a time-varying Geometric Brownian Motion model with a pricing mechanism used in financial engineering. Typical time series models such as Auto-Regressive…
Financial time series often exhibit skewness and heavy tails, making it essential to use models that incorporate these characteristics to ensure greater reliability in the results. Furthermore, allowing temporal variation in the skewness…