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Financial modeling with frictions is an area of research that challenges the traditional assumption of frictionless markets, which has long been a cornerstone in both academic and industry approaches. Empirical evidence and the actual mechanisms of financial markets reveal that this assumption is rarely met. Market frictions, which include transaction costs, taxes, regulatory costs, asset indivisibility, non-tradability, illiquidity, agency and information problems, and discrete-time trading mechanisms, significantly impact the stochastic nature of state variables, asset price trajectories, and the persistence of time series. These frictions necessitate the development of more sophisticated mathematical models that can account for market incompleteness, leading to the non-uniqueness of the equivalent martingale measure and requiring generalizations of the classical no-arbitrage principle. Despite ongoing research, there remains a gap in creating models that are both mathematically rigorous and economically realistic, particularly in addressing issues like unhedgeable risk and optimal wealth allocation.

This Research Topic aims to provide solutions that are rigorous from a mathematical point of view and realistic from an economic perspective, to address classic problems in finance such as arbitrage-free derivative pricing and portfolio optimization. The main objectives include answering specific questions related to optimal control problems with frictions, derivative pricing in non-frictionless markets, and decisions under partial and asymmetric information. Additionally, the scope encompasses research related to risk management, market impact analysis, and the application of machine learning in non-frictionless markets.

To gather further insights into the complexities of financial modeling with frictions, we welcome articles addressing, but not limited to, the following themes:
- Optimal control problems with frictions
- Derivative pricing in non-frictionless markets
- Decisions under partial information and asymmetric information
- Risk management with frictions
- Machine learning in non-frictionless markets
- Market impact analysis
- Optimal execution algorithms in the presence of market frictions
- Fractal tools and roughness modeling in finance

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Frontiers in Applied Mathematics and Statistics

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