Related papers: Valuation equations for stochastic volatility mode…
We investigate stochastic Volterra equations and their limiting laws. The stochastic Volterra equations we consider are driven by a Hilbert space valued \Levy noise and integration kernels may have non-linear dependence on the current state…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
We study the smoothness of the upper and lower value functions of stochastic differential games in the framework of time-homogeneous (possibly degenerate) diffusion processes in a domain, under the assumption that the diffusion, drift and…
In an equity market model with "Knightian" uncertainty regarding the relative risk and covariance structure of its assets, we characterize in several ways the highest return relative to the market that can be achieved using nonanticipative…
Stochastic differential equation (SDE) models are the foundation for pricing and hedging financial derivatives. The drift and volatility functions in SDE models are typically chosen to be algebraic functions with a small number (less than…
The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only…
We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging…
We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is neither restricted to Markov processes (or semimartingales),…
In an incomplete semimartingale model of a financial market, we consider several risk-averse financial agents who negotiate the price of a bundle of contingent claims. Assuming that the agents' risk preferences are modelled by convex…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully examine the relation between the option prices, related partial…
We investigate the problem of pricing derivatives under a fractional stochastic volatility model. We obtain an approximate expression of the derivative price where the stochastic volatility can be composed of deterministic functions of time…
This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices…
In this paper we provide an extensive classification of one and two dimensional diffusion processes which admit an exact solution to the Kolmogorov (and hence Black-Scholes) equation (in terms of hypergeometric functions). By identifying…
Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
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…
The study of stochastic variational principles involves the problem of constructing fixed-endpoint and adapted variations of semimartingales. We provide a detailed construction of variations of semimartingales that are not only fixed at…
The aim of this paper is to give a stochastic representation for the solution to a natural extension of the Caputo-type evolution equation. The nonlocal-in-time operator is defined by a hypersingular integral with a (possibly…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…