Related papers: Financial markets with volatility uncertainty

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…

In this paper, we study the pricing of contracts in fixed income markets under volatility uncertainty in the sense of Knightian uncertainty or model uncertainty. The starting point is an arbitrage-free bond market under volatility…

We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of…

The target of this paper is to consider model the risky asset price on the financial market under the Knightian uncertainty, and pricing the ask and bid prices of the uncertain risk. We use the nonlinear analysis tool, i.e., G-frame work…

The integration and innovation of finance and technology have gradually transformed the financial system into a complex one. Analyses of the causesd of abnormal fluctuations in the financial market to extract early warning indicators…

We study time consistent dynamic pricing mechanisms of European contingent claims under uncertainty by using G framework introduced by Peng ([24]). We consider a financial market consisting of a riskless asset and a risky stock with price…

In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of…

We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii)…

In this paper, we consider the stochastic optimal control problems under model risk caused by uncertain volatilities. To have a mathematical consistent framework we use the notion of G-expectation and its corresponding G-Brwonian motion…

We study the Hull-White model for the term structure of interest rates in the presence of volatility uncertainty. The uncertainty about the volatility is represented by a set of beliefs, which naturally leads to a sublinear expectation and…

G-framework is presented by Peng [41] for measure risk under uncertainty. In this paper, we define fractional G-Brownian motion (fGBm). Fractional G-Brownian motion is a centered G-Gaussian process with zero mean and stationary increments…

This work considers a stochastic model in which the uncertainty is driven by a multidimensional Brownian motion. The market price of risk process makes the transition between real world probability measure and risk neutral probability…

Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free. In fact, such models violate even the weakest no-arbitrage…

In the past decades, advanced probabilistic methods have had significant impact on the field of finance, both in academia and in the financial industry. Conversely, financial questions have stimulated new research directions in probability.…

We study a financial market where the risky asset is modelled by a geometric It\^o-L\'{e}vy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which…

In this article we propose a study of market models starting from a set of axioms, as one does in the case of risk measures. We define a market model simply as a mapping from the set of adapted strategies to the set of random variables…

We study the emergence of instabilities in a stylized model of a financial market, when different market actors calculate prices according to different (local) market measures. We derive typical properties for ensembles of large random…

It is shown that absence of arbitrage opportunity in financial markets is a particular case of existence of uncertainty in decision system. Absence of arbitrage opportunity is considered in the sense of the Arrow-Debreu model of financial…

In this paper, we study term structure movements in the spirit of Heath, Jarrow, and Morton [Econometrica 60(1), 77-105] under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian…

G-expectation, as a sublinear expectation, provides a powerful framework for modeling uncertainty in financial markets. Motivated by the need for robust valuation under model uncertainty, this work develops a unified risk-neutral valuation…