Related papers: The potential approach in practice
We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic…
This paper introduces an information-based model for the pricing of storable commodities such as crude oil and natural gas. The model uses the concept of market information about future supply and demand as a basis for valuation. Physical…
In this paper analytic formulas for electricity derivatives are calculated. To this end, we assume that electricity spot prices follow a 3-regime Markov regime-switching model with independent spikes and drops and periodic transition…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
In this paper we consider a reduced-form intensity-based credit risk model with a hidden Markov state process. A filtering method is proposed for extracting the underlying state given the observation processes. The method may be applied to…
We describe a simple model for speculative trading based on adaptive behavior of economic agents.The adaptive behavior is expressed through a feedback mechanism for changing agents' stock-to-bond ratios, depending on the past performance of…
We consider a general method for the approximation of the distribution of a process conditioned to not hit a given set. Existing methods are based on particle system that are failable, in the sense that, in many situations , they are not…
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not…
The method of reduction of a Fredholm integral equation to the linear system is generalized to construction of a complex potential --- an analytic function in an infinite multiply connected domain with a simple pole at infinity which maps…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously…
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…
This paper proposes swaps on two important new measures of generalized variance, namely the maximum eigen-value and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for financial markets with…
This paper aims to provide a simple modelling of speculative bubbles and derive some quantitative properties of its dynamical evolution. Starting from a description of individual speculative behaviours, we build and study a second order…
In this paper we discuss a scaling approach to business fluctuations. Our starting point consists in recognizing that concepts and methods derived from physics have allowed economists to (re)discover a set of stylized facts which have to be…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
The purpose of the present paper is to incorporate stochastic interest rates into a matrix-approach to multi-state life insurance, where formulas for reserves, moments of future payments and equivalence premiums can be obtained as explicit…
The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the…
We introduce a general framework for measuring risk in the context of Markov control processes with risk maps on general Borel spaces that generalize known concepts of risk measures in mathematical finance, operations research and…
The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the…