A financial market model where agents can only trade using realistic  buy-and-hold strategies is considered. Minimal assumptions are made on the nature of the asset-price process - in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition, we establish that asset-prices have be semimartingales, as well as a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than equivalent martingale measures. Further, the utility maximization problem is considered and it is shown that using only buy-and-hold strategies, optimal utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well .
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the asset-price process - in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the "No Unbounded Profit with Bounded Risk" condition, we establish that asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than Equivalent Martingale Measures .
D
can only
A
combinations of
D
nature of the
R
No-Unbounded-Profit-with-Bounded-Risk (NUPBR)
"No Unbounded Profit with Bounded Risk"
R
be semimartingales, as well as
to be semimartingales. In a slightly more specialized case, we extend the previous result in
R
equivalent martingale measures. Further, the utility maximization problem is considered and it is shown that using only buy-and-hold strategies, optimal utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well
Equivalent Martingale Measures