Related papers: Arbitrage Problems with Reflected Geometric Browni…
In this paper, we showed that the no-arbitrage condition holds if the market follows the mixture of the geometric Brownian motion (GBM). The mixture of GBM can incorporate heavy-tail behavior of the market. It automatically leads us to…
We study the semimartingale properties for the generalized fractional Brownian motion (GFBM) introduced by Pang and Taqqu (2019) and discuss the applications of the GFBM and its mixtures to financial asset pricing. The GFBM is self-similar…
The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on…
While Indices, Index tracking funds and ETFs have grown in popularity during then last ten years, there are many structural problems inherent in Index calculation methodologies and the legal/economic structure of ETFs. These problems raise…
We introduce Hermite fractional financial markets, where market uncertainties are described by multidimensional Hermite motions. Hermite markets include as particular cases financial markets driven by multivariate fractional Brownian motion…
We study hedging and pricing of unattainable contingent claims in a non-Markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a Brownian motion and a…
As operators acting on the undetermined final settlement of a derivative security, expectation is linear but price is non-linear. When the market of underlying securities is incomplete, non-linearity emerges from the bid-offer around the…
We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be…
The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional…
This short note provides a systematic construction of market models without unbounded profits but with arbitrage opportunities.
The comparative statics of the optimal portfolios across individuals is carried out for a continuous-time complete market model, where the risky assets price process follows a joint geometric Brownian motion with time-dependent and…
This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded…
We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include…
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not…
Consider a financial market with nonnegative semimartingales which does not need to have a num\'{e}raire. We are interested in the absence of arbitrage in the sense that no self-financing portfolio gives rise to arbitrage opportunities,…
We study the existence of the numeraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numeraire portfolio generates a wealth process, with respect to which the relative wealth…
In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices…
In this study we prove the existence of statistical arbitrage opportunities in the Black-Scholes framework by considering trading strategies that consists of borrowing from the risk free rate and taking a long position in the stock until it…
We derive the arbitrage gains or, equivalently, Loss Versus Rebalancing (LVR) for arbitrage between \textit{two imperfectly liquid} markets, extending prior work that assumes the existence of an infinitely liquid reference market. Our…
In the presence of ambiguity on the driving force of market randomness, we consider the dynamic portfolio choice without any predetermined investment horizon. The investment criteria is formulated as a robust forward performance process,…