Related papers: Consistent price systems and face-lifting pricing …
We propose a minimal theory of non-linear price impact based on a linear (latent) order book approximation, inspired by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the…
We survey some new progress on the pricing models driven by fractional Brownian motion \cb{or} mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We…
Let $X^1,\ldots, X^d$ be sigma-martingales on $(\Omega,{\cal F}, P)$. We show that every bounded martingale (with respect to the underlying filtration) admits an integral representation w.r.t. $X^1,\ldots, X^d$ if and only if there is no…
We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of…
We establish the existence and characterization of a primal and a dual facelift - discontinuity of the value function at the terminal time - for utility-maximization in incomplete semimartingale-driven financial markets. Unlike in the…
In a market with transaction costs, the price of a derivative can be expressed in terms of (preconsistent) price systems (after Kusuoka (1995)). In this paper, we consider a market with binomial model for stock price and discuss how to…
We consider fractional Black-Scholes market with proportional transaction costs. When transaction costs are present, one trades periodically i.e. we have the discrete trading with equidistance $n^{-1}$ between trading times. We derive a non…
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…
Shot-Noise processes constitute a useful tool in various areas, in particular in finance. They allow to model abrupt changes in a more flexible way than processes with jumps and hence are an ideal tool for modelling stock prices, credit…
We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the…
In the quest for market mechanisms that are easy to implement, yet close to optimal, few seem as viable as posted pricing. Despite the growing body of impressive results, the performance of most posted price mechanisms however, rely…
We present a machine learning approach for finding minimal equivalent martingale measures for markets simulators of tradable instruments, e.g. for a spot price and options written on the same underlying. We extend our results to markets…
This paper deals with the super-replication of non path-dependent European claims under additional convex constraints on the number of shares held in the portfolio. The corresponding super-replication price of a given claim has been widely…
We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete-time markets with dividend-paying securities. Specifically, we show that the no-arbitrage condition under the efficient friction…
For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless "shadow market" that yields the same optimal strategy…
High Frequency Trading (HFT) represents an ever growing proportion of all financial transactions as most markets have now switched to electronic order book systems. The main goal of the paper is to propose continuous time equations which…
We consider the problem of finding a real valued martingale fitting specified marginal distributions. For this to be possible, the marginals must be increasing in the convex order and have constant mean. We show that, under the extra…
To any utility maximization problem under transaction costs one can assign a frictionless model with a price process $S^*$, lying in the bid/ask price interval $[\underline S, \bar{S}]$. Such process $S^*$ is called a \emph{shadow price} if…
The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to…
The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are…