A trading strategy is defined as follows: starting capital $v_0 = 5$ and 1 risky asset holdings $\varphi_t = 3W_t^2-3t$ where $W$ is a Wiener process. The problem is to find the probability of the value of the strategy at the end of period 1 is greater than zero, $\mathbb{P}(V_1>0)$

Now, $V_1=v_0+\int_0^13W_s^2-3t\,dW_s=W_1^3-3W_1+5$

But how do I calculate $\mathbb{P}(W_1^3-3W_1+5>0)$ or have I completely gone off track?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.