Risk Measures Taking Into Account Stopping Time

This paper studies the effect stopping time on risk measures and portfolio optimization problem when investors implement the stop strategy and utilize new risk measures such as Stop Point Probability CVaR (SPP-CVaR) and SPP-VaR. The SPP-CVaR and SPP-VaR measures can solve the problem of stochastic exit time of investors due to the use of stop strategy. Conditional density function of the price process and density of the time that first cross stop-profit point are considered instead of density of return in CVaR measure. Also, this conditional density function can consider for SPP-VaR by Monte-Carlo simulation. Since, SPP-CVaR and SPP-VaR are dependent on the stopping time, it will be shown that the SPP-CVaR and SPP-VaR measures are accurately than the traditional risk measures .