If the investor makes her decision based on the minimax regret approach, which decision should she take?

Question

BlackTom AI · Accepted Answer

The question concerns decision making under the minimax regret criterion. This method requires evaluating the regret for each possible action in every state of nature, then selecting the action whose worst-case (maximum) regret is as small as possible.
Option S: To assess candidate S, one would need the full regret matrix to see how much would be foregone in each state by choosing S versus the best alternative in that state. If, in the worst state, choosing S yields a high regret, it makes S less favorable under minimax regret. Without the matrix values, we can only say that S would only be preferred if its maximum regret is smaller than that of the other options, which would require evidence from the data.
Option U: Similar logic applies to U. Its suitability hinges on whether its maximum regret across all states is the smallest among all options. If the largest regret associated with U is bigger than that of the other alternatives, U would be disfavored under the minimax regret rule. The decision hinges on the comparative worst-case regret, not on intuition alone.
Option B: For B, applying minimax regret means examining how B performs relative to the best possible action in each state and identifying the largest shortfall (regret). If, after comparing across all states, B exhibits the smallest of these largest regrets, then B is the preferred choice under this criterion. The provided answer indicates that B achieves the minimax of regret, i.e., its worst-case regret is no larger than the worst-case regrets of S, U, or D.
Option D: With D, the decision would only be favored if its maximum regret across all states is the smallest among all options. If the data shows that some state yields a higher missed opportunity when choosing D compared to at least one of the other options, D would not be optimal under minimax regret. The key is how D’s worst-case regret stacks up against others.
In summary, minimax regret requires a state-by-state comparison of how much one sacrifices by choosing each option, then selecting the option with the smallest greatest regret. The given result identifies B as the choice that minimizes this worst-case regret across all states, implying B has the smallest maximum regret when the entire regret matrix is considered. The other options would be disfavored if their maximum regrets are larger in at least one state or overall.

If the investor makes her decision based on the minimax regret approach, which decision should she take?单项选择题

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