Related papers: Second order stochastic differential models for fi…
In this paper, we introduce the second-order Esscher pricing notion for continuous-time models. Depending whether the stock price $S$ or its logarithm is the main driving noise/shock in the Esscher definition, we obtained two classes of…
We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…
The dynamics of financial markets are driven by the interactions between participants, as well as the trading mechanisms and regulatory frameworks that govern these interactions. Decision-makers would rather not ignore the impact of other…
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following…
The main focus of this work is to understand the dynamics of non regulated markets. The present model can describe the dynamics of any market where the pricing is based on supply and demand. It will be applied here, as an example, for the…
Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is…
In this paper we study the dynamics of stochastic microorganism flocculation models. Given the strong influence of environmental and seasonal fluctuations that are present in these models, we propose a stochastic model that includes…
Stylized facts can be regarded as constraints for any modeling attempt of price dynamics on a financial market, in that an empirically reasonable model has to reproduce these stylized facts at least qualitatively. The dynamics of market…
It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect.…
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics is offering models of markets as complex systems, such as the gas-like model, able to predict money distributions…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
We study a two-dimensional McKean-Vlasov stochastic differential equation, whose volatility coefficient depends on the conditional distribution of the second component with respect to the first component. We prove the strong existence and…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
The development of stochastic thermodynamics during the last decades prompted the discovery of novel nonequilibrium relations refining our understanding of the second law in small fluctuating systems and its connection with information…
The main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach. The control system is governed by a stochastic…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
In this article we address the question whether it is possible to learn the differential equations describing the physical properties of a dynamical system, subject to non-conservative forces, from observations of its realspace…
Recent work has addressed the problem of inferring Langevin dynamics from data. In this work, we address the problem of relating terms in the Langevin equation to statistical properties, such as moments of the probability density function…
We explore the behavior in time of the energy exchange between a system of interest and its environment, together with its relationship to the non-Markovianity of the system dynamics. In order to evaluate the energy exchange we rely on the…
Statistical mechanics provides a useful analog for understanding the behavior of complex adaptive systems, including electric power markets and the power systems they intend to govern. Market-based control is founded on the conjecture that…