Derive Equation (1)

Consider an agent with an initial endowment xo and a planning horizon T > 0. At time t, let the dollar amount and number of shares allocated to the ith asset be respectively mi and Ni, i = 0,1,...,l, and the total wealth be Xt. If the agent's trading is self-financing, namely, 1 dx= Nids, i=0 then we can derive similarly the wealth equation (try it yourself!) dxt = (r+X+ + BT 7+)dt + 74 OzdWt, (1) Consider an agent with an initial endowment xo and a planning horizon T > 0. At time t, let the dollar amount and number of shares allocated to the ith asset be respectively mi and Ni, i = 0,1,...,l, and the total wealth be Xt. If the agent's trading is self-financing, namely, 1 dx= Nids, i=0 then we can derive similarly the wealth equation (try it yourself!) dxt = (r+X+ + BT 7+)dt + 74 OzdWt, (1)