Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1911.05122

A two-player portfolio tracking game

Moritz Voß
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the competition of two strategic agents for liquidity in the benchmark portfolio tracking setup of Bank, Soner, Voß (2017). Specifically, both agents track their own stochastic running trading targets while interacting through common aggregated temporary and permanent price impact à la Almgren and Chriss (2001). The resulting stochastic linear quadratic differential game with terminal state constraints allows for a unique and explicitly available open-loop Nash equilibrium. Our results reveal how the equilibrium strategies of the two players take into account the other agent's trading targets: either in an exploitative intent or by providing liquidity to the competitor, depending on the relation between temporary and permanent price impact. As a consequence, different behavioral patterns can emerge as optimal in equilibrium. These insights complement and extend existing studies in the literature on predatory trading models examined in the context of optimal portfolio liquidation games.

Explore related subjects

q-fin.MF

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Moritz Voß. 2022-07-06. A two-player portfolio tracking game. https://arxiv.org/abs/1911.05122

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fixed-Income Pricing and the Replication of Liabilities

This paper develops a model-free framework for static fixed-income pricing and the replication of liability cash flows. The absence of static arbitrage across a universe of fixed-income instruments is equivalent to the existence of a strictly positive discount curve reproducing all observed prices. Linear programming duality then identifies the least-cost super-replication price with the largest value that any admissible discount curve assigns to the liability, so that the resulting bounds are attained and cannot be improved. Complementary slackness confines over-replication to dates that the optimal discount vector prices at zero, and a least-cost portfolio matches the liability exactly at no fewer dates than the rank of the cash-flow matrix. We also obtain generic uniqueness of that portfolio, an interpolation between quadratic hedging and super-replication, and a static treatment of swap--repo strategies. On US Treasury cross-sections the observed prices violate the law of one price, so that a discount curve must be estimated rather than bootstrapped; the least-cost portfolio then matches an annuity liability at almost every cash-flow date.

q-fin.MF↗
arXiv2026

Gatheral's Conjecture Revisited

We consider the Heston model with perfect negative spot--variance correlation and its one-dimensional local-volatility projection. Let $I_T^{\mathrm H}$ and $I_T^{\mathrm{LV}}$ denote their respective integrated variances over $[0,T]$. We establish the inequality \[ \mathbb{E}\bigl[(I_T^{\mathrm H}-K)^+\bigr] < \mathbb{E}\bigl[(I_T^{\mathrm{LV}}-K)^+\bigr] \] for every maturity $T>0$ and every strike $K>0$. Consequently, Heston integrated variance is strictly smaller in convex order than the integrated variance of the calibrated local-volatility model. This strict ordering gives a Heston-model counterexample to the convex-order inequality conjectured by J. Gatheral.

q-fin.MF↗
arXiv2026

Concave Shape of the Yield Curve and No Arbitrage

In fixed income sector, the yield curve is probably the most observed indicator by the market for trading and fifinancing purposes. A yield curve plots interest rates across different contract maturities from short end to as long as 30 years. For each currency, the corresponding curve shows the relation between the level of the interest rates (or cost of borrowing) and the time to maturity. For example, the U.S. dollar interest rates paid on U.S. Treasury securities for various maturities are plotted as the US treasury curve. For the same currency, if the swap market is used, we could also plot the swap rates across the tenors which would be called the swap curve.Even the yield curve can be at, upward or downward (inverted), however, yield curve is generally concave. There is a lack of explanation of the concavity of the yield curve shape from economics theory. We offer in this article an explanation of the concavity shape of the yield curve from trading perspectives.

q-fin.MF↗