= Supermartingale control of deflated consumption gains
{title2=$M_t=Y_tX_t-Y_0X_0+\int_0^tY_sc_sds$}
If wealth and <consumption> are nonnegative, this <local martingale> is bounded below by minus the finite initial deflated capital. Adding that capital gives a nonnegative <local martingale>, hence a <supermartingale> by the <Conditional Fatou lemma>. Consequently expected discounted <consumption> cannot exceed initial deflated wealth. The <consumption> sign and <predictable> stochastic <integrability> are part of the hypotheses.
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