Research notes

Bayesian Approaches to Sequential Decision Making in Uncertain Environments

Classical bet sizing rules like the Kelly criterion are optimal when markets are stationary and fail badly when the regime shifts without warning. I formalize why: a Bayesian agent that has learned one regime carries so much accumulated posterior mass that it keeps betting as if the old regime holds, and needs roughly as many new observations as it already had before its beliefs move. I call this the Sticky Prior Paradox and prove how large the lag is. I then propose two fixes. The first augments a hidden Markov regime filter with rolling volatility and a CUSUM change point trigger, which cuts regime detection lag from roughly 15 to 20 steps down to about 2. The second wraps Kelly sizing in a CPPI drawdown floor that provably caps the worst drawdown at a chosen level, and I measure the exact growth given up to buy that safety. Tested across three synthetic regimes and four S&P 500 crisis periods with realistic transaction costs; the volatility augmented filter significantly reduces ruin probability under the harshest shocks (Fisher exact test, p < 0.05).