medium · Quantitative Finance stochastic
If M_t is a martingale and h is a bounded, predictable strategy, why is the 'stochastic integral' (h · M)_t = int_0^t h_s dM_s also a martingale?
- The integral of any function is always zero in expectation.
- The strategy h must be a constant to preserve the martingale property.
- The volatility of M is neutralized by the strategy h.
- You cannot make money from a fair game by changing your bet size based on past information.
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