Equilibrium Strategies for Alpha-Maxmin Expected Utility Maximization
Bibliographic record
Abstract
In the existing literature of robust utility maximization with ambiguity, agents are generally assumed to be extremely ambiguity-averse as they tend to only consider expected payoffs in the worst-case scenario. However, experimental studies have shown that agents' attitude to ambiguity is not systematically negative and can even be ambiguity-seeking when they consider themselves knowledgeable or competent. To conceptually distinguish between an agent's perception of ambiguity and ambiguity aversion, the so-called $\alpha$-maxmin expected utility ($\alpha$-MEU) was proposed in the economics literature as a linear aggregation of the most and least favorable prior beliefs. Although the axiomatic characterization of $\alpha$-MEU has been well studied, there has been little work on the benchmark maximization problem for $\alpha$-MEU. The main difficulty stems from the dynamic inconsistency of two distinct extreme priors and nonconvexity (and nonconcavity) of the value function. In this paper, we study the maximization problem for $\alpha$-MEU and solve for the equilibrium strategies of open-loop type. Under logarithmic risk preference, we obtain the explicit form of equilibrium investment strategies, which involves a two-dimensional system of fully coupled quadratic backward stochastic differential equations (BSDE). The main challenge in completing the verification theorem is to study the existence, uniqueness, and stability of this system of BSDE. For this purpose, we consider a general Markov model of the financial market, which leads to a system of quadratic Markovian BSDE. We find that the equilibrium investment strategy becomes more conservative if the agent is more ambiguity-averse or the agent perceives more ambiguity in the financial market. The equilibrium strategy is close to the classical nonrobust strategy (without ambiguity) if the agent is ambiguity-neutral. As time approaches maturity, ambiguity-seeking (ambiguity-averse) agents adopt more aggressive (conservative) equilibrium strategies. Additionally, the equilibrium strategy of an ambiguity-neutral agent converges to the classical nonrobust strategy at maturity.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".