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In an incomplete semimartingale model of a financial market, we consider several risk-averse financial agents who negotiate the price of a bundle of contingent claims. Assuming that the agents' risk preferences are modelled by convex…
We analyse derivative securities whose value is NOT a deterministic function of an underlying which means presence of a basis risk at any time. The key object of our analysis is conditional probability distribution at a given underlying…
In a financial market model, we consider the variance-optimal semi-static hedging of a given contingent claim, a generalization of the classic variance-optimal hedging. To obtain a tractable formula for the expected squared hedging error…
A market model in Stochastic Portfolio Theory is a finite system of strictly positive stochastic processes. Each process represents the capitalization of a certain stock. If at any time no stock dominates almost the entire market, which…
This paper examines replication portfolio construction in incomplete markets - a key problem in financial engineering with applications in pricing, hedging, balance sheet management, and energy storage planning. We model this as a…
Shorting for hedging exposes to risk when the market dynamics is uncertain. Managing uncertainty and risk exposure is key in portfolio management practice. This paper develops a robust framework for dynamic minimum-variance hedging that…
We study the approximation of certain stochastic integrals with respect to a d-dimensional diffusion by corresponding stochastic integrals with piece-wise constant integrands. In finance this corresponds to replacing a continuously adjusted…
Convergence (virtual) bidding is an important part of two-settlement electric power markets as it can effectively reduce discrepancies between the day-ahead and real-time markets. Consequently, there is extensive research into the bidding…
The matter of the stability for multi-asset American option pricing problems is a present remaining challenge. In this paper a general transformation of variables allows to remove cross derivative terms reducing the stencil of the proposed…
We study the upper hedging price for contingent claims in market models with strong types of arbitrage: increasing profit, strong arbitrage, and arbitrage of the first kind. The existence of arbitrage may make the price smaller than if it…
The possibility of statistical evaluation of the market completeness and incompleteness is investigated for continuous time diffusion stock market models. It is known that the market completeness is not a robust property: small random…
In Bell scenario, any nonlocal correlation, shared between two spatially separated parties, can be modeled deterministically either by allowing communications between the two parties or by restricting their free will in choosing the…
We consider the design of private prediction markets, financial markets designed to elicit predictions about uncertain events without revealing too much information about market participants' actions or beliefs. Our goal is to design market…
We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function we adopt a g-expectation. In contrast to the standard framework of financial engineering,…
In real data analysis, the underlying model is usually unknown, modelling strategy plays a key role in the success of data analysis. Stimulated by the idea of model averaging, we propose a novel semiparametric modelling strategy for…
When agents trade in a Duality-based Cost Function prediction market, they collectively implement the learning algorithm Follow-The-Regularized-Leader. We ask whether other learning algorithms could be used to inspire the design of…
In this paper, we prove the global risk optimality of the hedging strategy of contingent claim, which is explicitly (or called semi-explicitly) constructed for an incomplete financial market with external risk factors of non-Gaussian…
We design three continuous--time models in finite horizon of a commodity price, whose dynamics can be affected by the actions of a representative risk--neutral producer and a representative risk--neutral trader. Depending on the model, the…
This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our…
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…