Testing by betting while borrowing and bargaining
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摘要
Testing by betting extends the classical sequential testing framework to allow borrowing against wealth, and derives two core results: (i) using a simple threshold Wt ≥ g(α, Lt) forces g(α, 0) > 1/α if any positive liability can be borrowed, meaning a price is paid for potential borrowing; (ii) using a path-dependent threshold h(α, W0, L1, ..., Wt−1, Lt) can recover the 1/α level with finite thresholds without paying the above price, but may sacrifice accumulated evidence after bankruptcy. These findings illuminate fundamental trade-offs between borrowing flexibility and error-control in testing by betting [page::0].
