arXiv subjects

Jingzhi Tie

Publications and source records attributed to Jingzhi Tie.

4 recordsLinked to original sources

arXiv2023

Optimal Strategies for Round-Trip Pairs Trading Under Geometric Brownian Motions

This paper is concerned with an optimal strategy for simultaneously trading a pair of stocks. The idea of pairs trading is to monitor their price movements and compare their relative strength over time. A pairs trade is triggered by the divergence of their prices and consists of a pair of positions to short the strong stock and to long the weak one. Such a strategy bets on the reversal of their price strengths. A round-trip trading strategy refers to opening and closing such a pair of security positions. Typical pairs-trading models usually assume a difference of the stock prices satisfies a mean-reversion equation. However, we consider the optimal pairs-trading problem by allowing the stock prices to follow general geometric Brownian motions. The objective is to trade the pairs over time to maximize an overall return with a fixed commission cost for each transaction. Initially, we allow the initial pairs position to be either long or flat. We then consider the problem when the initial pairs position may be long, flat, or short. In each case, the optimal policy is characterized by threshold curves obtained by solving the associated HJB equations.

math.OC↗

arXiv2023

Pairs Trading: An Optimal Selling Rule with Constraints

The focus of this paper is on identifying the most effective selling strategy for pairs trading of stocks. In pairs trading, a long position is held in one stock while a short position is held in another. The goal is to determine the optimal time to sell the long position and repurchase the short position in order to close the pairs position. The paper presents an optimal pairs-trading selling rule with trading constraints. In particular, the underlying stock prices evolve according to a two dimensional geometric Brownian motion and the trading permission process is given in terms of a two-state {trading allowed, trading not allowed} Markov chain. It is shown that the optimal policy can be determined by a threshold curve which is obtained by solving the associated HJB equations (quasi-variational inequalities). A closed form solution is obtained. A verification theorem is provided. Numerical experiments are also reported to demonstrate the optimal policies and value functions.

q-fin.MF↗

arXiv2022

The Kohn-Laplacian and Cauchy-Szegö projection on Model Domains

We study the Kohn-Laplacian and its fundamental solution on some model domains in $\mathbb C^{n+1}$, and further discuss the explicit kernel of the Cauchy-Szegö projections on these model domains using the real analysis method. We further show that these Cauchy-Szegö kernels are Calderón-Zygmund kernels under the suitable quasi-metric.

math.CV↗

arXiv2018

CR Sub-Laplacian Comparison and Liouville-type Theorem in a Complete Noncompact Sasakian Manifold

In this paper, we first obtain the sub-Laplacian comparison theorem in a complete noncompact pseudohermitian manifold of vanishing torsion (i.e. Sasakian manifold). Secondly, we derive the sub-gradient estimate for positive pseudoharmonic functions in a complete noncompact pseudohermitian manifold which satisfies the CR sub-Laplacian comparison property. It is served as the CR analog of Yau's gradient estimate. As a consequence, we have the natural CR analogue of Liouville-type theorems in a complete noncompact Sasakian manifold of nonnegative pseudohermitian Ricci curvature tensors.

math.AP↗