Related papers: Arbitrage Problems with Reflected Geometric Browni…
A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation, as they usually appear in frictionless…
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…
Value adjustment of uncollateralized trades is determined within a risk-neutral pricing framework. When hedging such trades, investors cannot freely trade protection on their own name, thus facing an incomplete market. This fact is…
We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic…
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.…
This note develops an arbitrage theory for a discrete-time market model without the assumption of the existence of a num\'eraire asset. Fundamental theorems of asset pricing are stated and proven in this context. The distinction between the…
We consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and…
Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing of illiquid derivatives and managing risks of option trade books. This paper develops a nonparametric model for the European options book respecting…
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage…
Financial models based on the Wick product, and White Noise formalism have previously been suggested in order to incorporate integrals with respect to fractional Brownian motion. It has also been pointed out that this leads naturally to a…
We construct and study market models admitting optimal arbitrage. We say that a model admits optimal arbitrage if it is possible, in a zero-interest rate setting, starting with an initial wealth of 1 and using only positive portfolios, to…
An innovative extension of Geometric Brownian Motion model is developed by incorporating a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian…
We revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure $\rho$. We first show that under mild assumptions, the set of optimal portfolios for a fixed return…
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…
We consider a limit order book, where buyers and sellers register to trade a security at specific prices. The largest price buyers on the book are willing to offer is called the market bid price, and the smallest price sellers on the book…
Option pricing is mainly based on ideal market conditions which are well represented by the Geometric Brownian Motion (GBM) as market model. We study the effect of non-ideal market conditions on the price of the option. We focus our…
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.…
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…
In this paper a finite discrete time market with an arbitrary state space and bid-ask spreads is considered. The notion of an equivalent bid-ask martingale measure (EBAMM) is introduced and the fundamental theorem of asset pricing is proved…
This paper studies the optimal investment problem with random endowment in an inventory-based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules…