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We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of…
The Mutual Fund Theorem (MFT) is considered in a general semimartingale financial market S with a finite time horizon T, where agents maximize expected utility of terminal wealth. It is established that: 1) Let N be the wealth process of…
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…
We give a definitive treatment of duality for optimal consumption over the infinite horizon, in a semimartingale incomplete market satisfying no unbounded profit with bounded risk (NUPBR). Rather than base the dual domain on (local)…
In this paper, we propose a novel method for matrix completion under general non-uniform missing structures. By controlling an upper bound of a novel balancing error, we construct weights that can actively adjust for the non-uniformity in…
We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with d traded assets. We introduce a plugin estimator based on empirical measures and show it is consistent but lacks suitable…
Financial markets are often modelled as if time were unique and continuous across assets and markets. Financial markets are however asynchronous, order flow is event-driven, and waiting times between events are often random. Many of the…
In this paper we investigate discrete time trading under integer constraints, that is, we assume that the offered goods or shares are traded in integer quantities instead of the usual real quantity assumption. For finite probability spaces…
We explore a decomposition in which returns on a large class of portfolios relative to the market depend on a smooth non-negative drift and changes in the asset price distribution. This decomposition is obtained using general continuous…
We develop a risk-neutral spot and equity option market simulator for a single underlying, under which the joint market process is a martingale. We leverage an efficient low-dimensional representation of the market which preserves no static…
The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
In this work we introduce the notion of fully incomplete markets. We prove that for these markets the super-replication price coincide with the model free super-replication price. Namely, the knowledge of the model does not reduce the…
For several decades, the no-arbitrage (NA) condition and the martingale measures have played a major role in the financial asset's pricing theory. We propose a new approach for estimating the super-replication cost based on convex duality…
We extend our studies of a quantum field model defined on a lattice having the dilation group as a local gauge symmetry. The model is relevant in the cross-disciplinary area of econophysics. A corresponding proposal by Ilinski aimed at…
This review summarizes the historical development of probability measures in asset pricing, from early mathematical finance and state price theory to risk-neutral valuation, martingale measures, forward measures, stochastic discount…
Consider a financial market in which an agent trades with utility-induced restrictions on wealth. By introducing a general convex-analytic framework which includes the class of umbrella wedges in certain Riesz spaces and faces of convex…
We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show…
We propose an optimal portfolio problem in the incomplete market where the underlying assets depend on economic factors with delayed effects, such models can describe the short term forecasting and the interaction with time lag among…
We consider a market model where there are two levels of information. The public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can…