Table of Links
- The Model Set-up
- Price Impact in a Market with No Transaction Costs
- Price Impact in a Market with Transaction Costs
Appendix A. Proofs of Section 3
Appendix B. Proofs of Section 4
Appendix B. Proofs of Section
Proof of Corollary 4.7. Under transaction costs, the market-clearing condition holds for both the investors’ demands and trading rates. Now, following similar steps as the ones we did to derive the price-impact process (41), we may use (26) for the strategic investor n and get:
where µ is the frictionless competitive equilibrium returns. Uniqueness follows from the uniqueness of the frictional best-response strategy for investor n, as well as from the uniqueness of the competitive frictional strategies for the rest of the investors. Now, recalling (15) and noting that the above is a linear combination of processes in H∞, we get the desired result.
Proof of Theorem 4.12. The steps for this proof are similar to the ones of Lemma 4.3, Proposition 4.5, Proposition 4.6, Lemma 4.9 and Theorem 4.10. Thus, we omit a part of the analysis and refer to the original proofs for more details.
We first consider the price-impact process of investor 1. As in Lemma 4.3, the respective form of (41) in this case is given as:
Using similar arguments as with (43) and (45) in Lemma 4.3, the adjusted frictional objective functional under investor 1’s price impact becomes:
Authors:
(1) Michail Anthropelos;
(2) Constantinos Stefanakis.
This paper is
