Related papers: Consistent price systems and face-lifting pricing …
In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these…
Let $M$ be a von Neumann algebra and let $(N_t)_{t\in[0,T]}$ be an increasing family of abelian von Neumann subalgebras encoding a (classical) information flow. Fix a faithful normal state $\varphi_\rho$ and a filtration of normal…
First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere as nonlinear diffusion or diffusion with nonlinear feedback.…
In this paper we study dynamic pricing mechanism of contingent claims. A typical model of such pricing mechanism is the so-called g-expectation $E^g_{s,t}[X]$ defined by the solution of the backward stochastic differential equation with…
We consider a one-period market model composed by a risk-free asset and a risky asset with $n$ possible future values (namely, a $n$-nomial market model). We characterize the lower envelope of the class of equivalent martingale measures in…
A general diffusion semimartingale is a one-dimensional path-continuous semimartingale that is also a regular strong Markov process. We say that a continuous semimartingale has the representation property if all local martingales w.r.t. its…
We consider a financial model where the prices of risky assets are quoted by a representative market maker who takes into account an exogenous demand. We characterize these prices in terms of a system of BSDEs with quadratic growth. We show…
This paper develops a model for the bid and ask prices of a European type asset by formulating a stochastic control problem. The state process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend…
We consider the problem of option pricing and hedging when stock returns are correlated in time. Within a quadratic-risk minimisation scheme, we obtain a general formula, valid for weakly correlated non-Gaussian processes. We show that for…
In a discrete-time financial market, a generalized duality is established for model-free superhedging, given marginal distributions of the underlying asset. Contrary to prior studies, we do not require contingent claims to be upper…
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…
Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative…
How do we assign value to economic transactions? To answer this question, we must consider whether the value of objects is inherent, is a product of social interaction, or involves other mechanisms. Economic theory predicts that there is an…
We study the global fluctuations for a class of determinantal point processes coming from large systems of non-colliding processes and non-intersecting paths. Our main assumption is that the point processes are constructed by biorthogonal…
It is well known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. In the present paper we consider the inverse problem, that is, given prices of perpetual American…
We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an…
Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction…
We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, this was proven for the…
For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised…
In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and…