Financial Modeling with Frictions

Most approaches in both academia and industry assume the absence of frictions as one of the main premises in modeling financial markets. However, both empirical evidence and the actual working mechanisms of markets show that this premise is far from being fulfilled. Market frictions can be categorized in a variety of ways, and comprise transaction costs, taxes, explicit or implicit regulatory costs, the indivisibility feature of assets, assets’ non-tradability and illiquidity, the presence of agency and information problems, different funding and adjustment rates, and discrete-time trading mechanisms. These frictions are responsible for the stochasticity of the state variables governing the market, the irregularity of the asset prices’ trajectories, the persistence (or otherwise) of the corresponding time series, and the presence of a long memory of the probability distributions representing them.

Such considerations dictate the need to introduce more sophisticated mathematical models able to incorporate the above-mentioned features. In so doing, one of the basic assumptions of financial models – namely, market completeness – is missing. In mathematical terms, this translates into the non-uniqueness of the equivalent martingale measure, paving the way for the need of generalizations of the classical no-arbitrage principle.

In terms of applications, market incompleteness acts on several levels, ranging from the need for derivatives traders to manage unhedgeable risk, to the complications investors face when they aim to choose optimal wealth allocation or consumption strategies.

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. Topics of interest include, but are not limited to, the following:

- 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

Keywords: frictions, finance, insurance, pricing, trading, roughness, optimal control

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