bv_cvxbook_extra_exercises

# In that case we lose rij xj ie our net is gain rij xj

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: shares of the asset. Here you sell shares at the bid price, up to the quantity q buy (or −q , whichever is smaller); if needed, you sell shares at the price pbuy , and so on, until all −q shares are sold. Here 2 buy buy we assume that −q ≤ q1 + · · · + qM , i.e., you are not selling more shares than the total quantity of oﬀers to buy. Let A denote the amount you receive from the sale. Here we deﬁne the transaction cost as T (q ) = −pmid q − A, the diﬀerence between the amount you would have received had you sold the shares at the mid-price, and the amount you received. It is always positive. We set T (0) = 0. (a) Show that T is a convex piecewise linear function. (b) Show that T (q ) ≥ (s/2)|q |, where s is the spread. When would we have T (q ) = (s/2)|q | for all q (in the range between the total shares oﬀered to purchase or sell)? (c) Give an interpretation of the conjugate function T ∗ (y ) = supq (yq − T (q )). Hint. Suppose you can purchase or sell the asset in another market, at the price pother . 103 13.2...
View Full Document

Ask a homework question - tutors are online