I am wondering whether there is a standard procedure to find a non attainable (i.e. non replicable) asset in an incomplete market. As an example, let us have the following market ($B = (B^1, B^2, B^3)$ is a $\mathbb{P}$-SBM): $$dX_t^0 = 0 \\ dX_t^1 = dt + dB_t^1 + dB_t^2 - dB_t^3 \\ dX_t^2 = 5dt - dB_t^1 + dB_t^2 + dB_t^3$$ This is clearly incomplete (number of risky assets is less than dimension of the underlying brownian motion), which means a non attainable claim exists.
How do I find such a claim? What should I look for?


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