Related papers: Martingale Representation Theorem for the G-expect…
The objective of this paper is to derive a representation of symmetric G-martingales as stochastic integrals with respect to the G-Brownian motion. For this end, we first study some extensions of stochastic calculus with respect to…
By the classical Martingale Representation Theorem, replication of random vectors can be achieved via stochastic integrals or solutions of stochastic differential equations. We introduce a new approach to replication of random vectors via…
We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations. Our approach relies on comparison results for forward-backward stochastic…
Let $X$ be a point process and let $\mathbb{X}$ denote the filtration generated by $X$. In this paper we study martingale representation theorems in the filtration $\mathbb{G}$ obtained as an initial and progressive enlargement of the…
The aim of this paper is to introduce a new formalism for the deterministic analysis associated with backward stochastic differential equations driven by general c{\`a}dl{\`a}g martingales. When the martingale is a standard Brownian motion,…
We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for…
This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a num\'eraire. It is shown that the presence of arbitrarily small…
We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function we adopt a g-expectation. In contrast to the standard framework of financial engineering,…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued…
The objective of this paper is to establish the decomposition theorem for supermartingales under the $G$-framework. We first introduce a $g$-nonlinear expectation via a kind of $G$-BSDE and the associated supermartingales. We have shown…
Consider $\mathbb{G}$ the progressive enlargement of a filtration $\mathbb{F}$ with a random time $\tau$. Assuming that, in $\mathbb{F}$, the martingale representation property holds, we examine conditions under which the martingale…
By using a simple observation that the density processes appearing in Ito's martingale representation theorem are invariant under the change of measures, we establish a non-linear version of the Cameron-Martin formula for solutions of a…
Our purpose is to prove the uniqueness of the representation for $G$-martingales with finite variation.
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the…
Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets…
We investigate financial markets under model risk caused by uncertain volatilities. For this purpose we consider a financial market that features volatility uncertainty. To have a mathematical consistent framework we use the notion of…
In this paper, we address the stochastic representation problem in discrete time under (non-linear) g-expectation. We establish existence and uniqueness of the solution, as well as a characterization of the solution. As an application, we…
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically…
We generalise the martingale-coboundary representation of discrete time stochastic processes to the non-stationary case and to random variables in Orlicz spaces. Related limit theorems (CLT, invariance principle, log log law, probabilities…
We give a bare-hands approach to the martingale representation theorem for integer valued random measures, which allows for a wide class of infinite activity jump processes, as well as all processes with well-ordered jumps.