Strategies for Combining and Coordinating Multiple Utility Functions in Algorithmic Trading: A Multi

Genetic algorithms, particle swarm optimization, and other group optimization techniques can be applied across multiple levels of decision-making processes, such as the strategic level for architecture search, the tactics level for utility function selection, and the operational level for specific function optimization paths.

The CRRA (Constant Relative Risk Aversion) utility function generally aligns with people's immediate perceptions, where utility depends on the proportional relationship between outcome and total assets. However, it can distort at extremely small or large total asset values. The CARA (Constant Absolute Risk Aversion) utility function is mathematically easier to handle, but its assumption of a constant level of risk aversion is somewhat distant from reality. The QPLs (Quantum Prospect Theory based Logarithmic Scoring rules) utility function, inspired by quantum financial theory, captures the non-linearity and probabilistic nature of markets. It discretizes continuous problems, thus reducing the action space and improving computational efficiency. Moreover, it naturally incorporates profit and loss factors, which might require additional constraints with other utility functions. But it necessitates prior knowledge about market distribution, which can vary across markets and over time.

From a market characteristics perspective, the CRRA utility function could be used for stock trading, the CARA utility function for bond trading, and the QPLs utility function for foreign exchange trading. From a temporal perspective, reference-dependent utility functions could be employed for short-term trading (with a daily/weekly target or reference point), while power utility functions tend to consider long-term overall returns.

Maximizing expected utility serves as the offense, minimizing risk or regret as the defense, and meeting certain constraints (not easily integrated into the former two) forms the "cage".

In the face of multiple utility functions, three strategies can be adopted: selection, integration into a single utility function, and combination. For a combination approach aiming for consistency and efficient coordination, methods include:

1. Weighted average when importance is at the same level.

2. Hierarchical structure when importance or priority is at different levels; this might require logical or a priori understanding of the problem framework.

3. Voting schemes where diverse utility function objectives aggregate under majority rule or consensus.

4. Fuzzy logic where each utility function is assigned a fuzzy weight, thus better capturing the uncertainty and ambiguity of the real world.

Academic papers, books, articles, and blogs on multi-objective optimization, multi-criteria decision making, ensemble learning, and multi-agent systems can be referred to for applications of combination or coordination methods.