Let E(K):$Z_0=0$ and $dZ_t=K_t(B_t-Z_t)dt+\alpha K_td \beta_t$ with B and $\beta$ two brownian motions, $\alpha>0$ and K a continue function.
1)Show that E(K) has a solution Z with $E(\int_0^1 Z_t^2 dt)<\infty$ 2) Show that E(K) has a unique solution: $Z^{(1)}$ and $Z^{(2)}$ are solution of E(K) with $Z_t^{(1)}=Z_t^{(2)}$ ps for all $t \in [0,1]$
For the question 1): I think to use the property in stong solutions but it's not possible because there is $B_t$
For the question 2) I don't know
Thank you