= State-price density and local deflator distinction
A <local martingale deflator> only forces deflated asset prices to be local martingales. True expectation pricing requires additional martingale and integrability properties. In a Brownian one-factor market, continuity of the coefficients ensures a pathwise finite market-price-of-risk square integral, but not expectation-one of its <stochastic exponential>. The <reciprocal three-dimensional Bessel strict local martingale> gives a counterexample to promoting this local conclusion automatically.
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