Before revision:  < t_n < s_n \leq b i=1^{n} \max } W_{t_i We prove that exponential moments of the above quantities are finite (in opposite to the regular variation, corresponding to TV^0, which is infinite almost surely). We present estimates of the expected value of \% UTV^c up to universal constants. As an application we give some estimates of the maximal possible gain from trading a financial asset in the presence of flat commission (proportional to the value of the transaction) when the dynamics of the prices of the asset follows a geometric Browniam motion process.
After revision:  < t_n < s_n \leq b i=1^{n} \max } W_{t_i . The defined quantities may have some interpretation in financial mathematics. Exponential moment of upward truncated variation may be interpreted as the maximal possible return from trading a financial asset in the presence of flat commission (proportional to the value of the transaction) when the dynamics of the prices of the asset follows a geometric Browniam motion process.