-
Optimal Investment with Quadratic Transaction Costs in a Multi-factor
and Stochastic Interest Rate Environment (with
and Qianyu
Liu).
Working Paper.
[Abstract|SSRN]
This paper studies an optimal investment problem in a comprehensive
market environment featuring geometric Brownian motion type asset
dynamics, stochastic interest rates, return and volatility factors,
and time-varying, state-dependent quadratic transaction costs. Under a
finite-horizon mean-quadratic variation objective, we derive a
semi-analytical solution for the value function and optimal trading
strategy and establish the well-posedness of the associated system of
nonlinear PDEs along with the verification theorem. The optimal
strategy retains a tractable structure that echoes the core economic
principle of trading gradually toward an aim portfolio as proposed in
Gârleanu and Pedersen (2013). Specifically, the aim portfolio is
adjusted for hedging demands against the interest rate risk, and the
trading speed reflects an intertemporal trade-off between immediate
rebalancing costs and future market liquidity. Additionally, we
propose a deep learning scheme to enable efficient implementation in
high-dimensional settings based on observable market data and
estimated factor models.
-
Arbitrage on Decentralized Exchanges (with
and
).
submitted. Updated: February 2026.
[Abstract|SSRN|arXiv]
First Place,
Student Best Paper Award, INFORMS Section on Finance, 2025.
Decentralized exchanges using automated market makers create arbitrage
opportunities with centralized exchanges, where gas fees and
transaction ordering are critical. Existing models largely overlook
competition among arbitrageurs, despite price discrepancies being
public information. We develop the first equilibrium model of gas fee
competition between two arbitrageurs under three transaction reversion
settings: no-revert, auto-revert, and selectable-revert. We show that
pure symmetric equilibria do not exist, but unique mixed equilibria
can be characterized. Comparative analysis reveals that under low
inventory risk, the no-revert setting favors arbitrageurs in terms of
profit, while auto-revert and selectable-revert settings enhance
market efficiency. Under high inventory risk, the no-revert and
selectable-revert settings dominate the auto-revert setting in both
profitability and efficiency. Using data from Binance and Uniswap V2,
we empirically confirm that arbitrageurs face positive inventory risk
and validate our model's implications: gas fees increase with price
discrepancies and liquidity, while trading amounts rise with both
price discrepancies and gas fees.
-
Periodic Evaluation with Non-Concave Utility (with
and
).
submitted.
[Abstract|SSRN]
A fund manager's performance is often evaluated annually and compared
with a benchmark, such as a market index. In addition, the manager may
be subject to trading constraints, such as limited use of leverage, no
short-selling, and a forced liquidation clause. We formulate this as a
periodic evaluation problem with a non-concave utility, a stochastic
reference point, and trading constraints. The value function is
characterized as the unique solution to a Hamilton-Jacobi-Bellman
equation with periodic terminal and boundary conditions, which must be
imposed carefully due to possible discontinuities at the terminal time
and/or on the liquidation boundary. We find that, at the evaluation
time, future investment opportunities induce a discontinuity in the
value function on the liquidation boundary, leading to a substantial
change in local risk-aversion. More importantly, this local
concavity/convexity weakens and shifts inward from the liquidation
boundary to the interior region as the evaluation horizon increases.
As a result, the joint effect of periodic evaluation and forced
liquidation can generate highly nonlinear investment strategies, which
is helpful in understanding the complexity of trading strategies in
the loss region.
-
Pricing Model for Data Assets in Investment-Consumption Framework with
Ambiguity (with
and
).
submitted.
[Abstract|SSRN|arXiv]
Data assets are data commodities that have been processed, produced,
priced, and traded based on actual demand. Reasonable pricing
mechanism for data assets is essential for developing the data market
and realizing their value. Most existing literature approaches data
asset pricing from the seller's perspective, focusing on data
properties and collection costs, however, research from the buyer's
perspective remains scarce. This gap stems from the nature of data
assets: their value lies not in direct revenue generation but in
providing informational advantages that enable enhanced
decision-making and excess returns. This paper addresses this gap by
developing a pricing model based on the informational value of data
assets from the buyer's perspective. We determine data asset prices
through an implicit function derived from the value functions in two
robust investment-consumption problems under ambiguity markets via
indifference pricing principle. By the existing research results, we
simplify the value function, using mathematical analysis and
differential equation theory, we derive general expressions for data
assets price and explore their properties under various conditions.
Furthermore, we derive the explicit pricing formulas for specific
scenarios and provide numerical illustration to describe how to use
our pricing model.
-
Arbitrage in Perpetual Contracts (with
Min Dai
and
Linfeng Li).
submitted. Updated: September 2025.
[Abstract|SSRN]
Perpetual contracts, designed to track the underlying price through a
funding swap mechanism, have gained significant popularity in
cryptocurrency markets. However, observed price discrepancies between
perpetual contracts and the underlying asset cannot be explained
solely by transaction fees. By examining the impact of the clamping
function inherent in the funding swap mechanism -- an overlooked
aspect in existing literature -- we derive model-free no-arbitrage
bounds for perpetual contracts. Our findings reveal that these bounds
persist as intervals even without transaction fees, due to the
clamping function. Empirical analysis using two years of Binance data
supports the validity of our proposed bounds.
-
Optimal Design of Automated Market Makers on Decentralized Exchanges
(with and
).
submitted.
[Abstract|SSRN|arXiv]
Automated market makers are a popular mechanism used on decentralized
exchange, through which users trade assets with each other directly
and automatically through a liquidity pool and a fixed pricing
function. The liquidity provider contributes to the liquidity pool by
supplying assets to the pool, and in return, they earn trading fees
from investors who trade in the pool. We propose a model of optimal
liquidity provision in which a risk-averse liquidity provider decides
the amount of wealth she would invest in the decentralized market to
provide liquidity in a two-asset pool, trade in a centralized market,
and consume in multiple periods. We derive the liquidity provider's
optimal strategy and the optimal design of the automated market maker
that maximizes the liquidity provider's utility. We find that the
optimal unit trading fee increases in the volatility of the
fundamental exchange rate of the two assets. We also find that the
optimal pricing function is chosen to make the asset allocation in the
liquidity pool efficient for the liquidity provider.
-
Calibration of Local Volatility Models under the Implied Volatility
Criterion (with
,
, and
).
submitted.
[Abstract|SSRN]
We study non-parametric calibration of local volatility models, which
is formulated as an inverse problem of partial differential equations
with Tikhonov regularization. In contrast to the existing literature
minimizing the distance between theoretical and market prices of
options as a calibration criterion, we instead minimize the distance
between theoretical and market implied volatilities, complying with
market practices. We prove that our calibration criterion naturally
leads to the well-posedness of the calibration problem. In particular,
comparing to Jiang and Tao (2001), we obtain a global uniqueness
result, where no additional weight functions are required. Numerical
results reveal that our method achieves a better trade-off between
minimizing calibration errors and reducing overfitting.
-
Patience is a Virtue: Optimal Investment in the Presence of Market
Resilience (with
,
, and Qiheng
Ding).
submitted. Updated: July 2025.
[Abstract|SSRN]
This paper investigates an optimal investment problem in an illiquid
market, modeling explicitly the effects of three key features of
market microstructure --- market tightness, market depth, and finite
market resilience --- on the investor's decision. By employing a
Bachelier process to model the dynamic of the fundamental value of the
asset and assuming CARA-type utility for the investor, we obtain the
investor's optimal dynamic trading strategy in closed form by solving
the resulting high-dimensional singular control problem. Furthermore,
we extend the model to incorporate return-predicting signals and
utilize an asymptotic expansion approach to derive approximate optimal
trading strategies. The theoretical and numerical results emphasize
the vital role of patience. Specifically, rather than dispersing small
trades continuously over time as advocated by the existing literature,
our findings suggest that investors should strategically time their
trading activities jointly based on market liquidity and market
signal. To quantify this timing decision, we introduce a patience
index that enables investors to strike a balance among various
competing goals, including achieving currently optimal risk exposure,
incorporating signals about future predictions, and minimizing trading
costs, by leveraging market resilience. We also demonstrate how to
implement our patient trading strategy using real-life market data.
-
Non-Concave Utility Maximization with Transaction Costs (with
).
SIAM Journal on Financial Mathematics, 17(2):406-449, 2026.
[Abstract|SSRN|arXiv|Article]
This paper studies a finite-horizon portfolio selection problem with
non-concave terminal utility and proportional transaction costs. The
commonly used concavification principle for terminal value is no
longer valid here, and we establish a proper theoretical
characterization of this problem. We first give the asymptotic
terminal behavior of the value function, which implies any transaction
close to maturity only provides a marginal contribution to the
utility. After that, the theoretical foundation is established in
terms of a novel definition of the viscosity solution incorporating
our asymptotic terminal condition. Via numerical analyses, we find
that the introduction of transaction costs into non-concave utility
maximization problems can prevent the portfolio from unbounded
leverage and make a large short position in stock optimal despite a
positive risk premium and symmetric transaction costs.
-
Optimal Tax-Timing with Transaction Costs (with
, Yaoting Lei,
and ).
Management Science, Accepted for Publication.
[Abstract|SSRN|Article]
We develop a dynamic portfolio model incorporating capital gains tax
(CGT), transaction costs, and year-end taxation. We find that even
tiny transaction costs can lead to significant deferral of large
losses and transaction costs affect loss deferrals much more than gain
deferrals. Our model can thus help explain the puzzle that even when
investors face equal long-term/short-term CGT rates, they may still
defer realizing large capital losses for an extended period of time,
displaying the disposition effect. In addition, we find misestimating
transaction costs is costly. We also provide several unique,
empirically testable predictions and shed light on recently proposed
tax policy changes.
-
Designing Stablecoins (with
,
,
, and
).
Mathematical Finance, 35(1):263-294, 2025.
[Abstract|SSRN|Article]
Stable coins, which are cryptocurrencies pegged to other stable
financial assets such as U.S. dollar, are desirable for payments
within blockchain networks, whereby being often called the “Holy Grail
of cryptocurrency.” However, existing cryptocurrencies are too
volatile for these purposes. By using the option pricing theory, we
design several dual-class structures that offer a fixed income crypto
asset, a stable coin pegged to a traditional currency, and leveraged
investment instruments. To understand the impact of the proposed coins
on the speculative and non-speculative demands of cryptocurrencies, we
study equilibrium with and without the stable coins. Our investigation
of the values of stable coins in presence of jump risk and black-swan
type events shows the robustness of the design.
-
An Equilibrium Model for the Cross Section of Liquidity Premia (with
and
).
Mathematics of Operations Research, 48(3):1423-1453, 2023.
[Abstract|SSRN|arXiv|Article]
We study a risk-sharing economy where an arbitrary number of
heterogenous agents trades an arbitrary number of risky assets subject
to quadratic transaction costs. For linear state dynamics, the
forward-backward stochastic differential equations characterizing
equilibrium asset prices and trading strategies in this context reduce
to a system of matrix-valued Riccati equations. We prove the existence
of a unique global solution and provide explicit asymptotic expansions
that allow us to approximate the corresponding equilibrium for small
transaction costs. These tractable approximation formulas make it
feasible to calibrate the model to time series of prices and trading
volume, and to study the cross-section of liquidity premia earned by
assets with higher and lower trading costs. This is illustrated by an
empirical case study.
-
Leveraged Exchange-Traded Funds with Market Closure and Frictions (with
,
, and
).
Management Science, 69(4):2517-2535, 2023.
[Abstract|SSRN|Article]
Although leveraged ETFs are popular products for retail investors, how
to hedge them poses a great challenge to financial institutions. We
develop an optimal rebalancing (hedging) model for leveraged ETFs in a
comprehensive setting, including overnight market closure and market
frictions. The model allows for an analytical optimal rebalancing
strategy. The result extends the principle of "aiming in front of
target" introduced by
Gârleanu and Pedersen (2013)
from a constant weight between current and future positions to a
time-varying weight, because the rebalancing performance is monitored
only at discrete time points but the rebalancing takes place
continuously. Empirical findings and implications for the weekend
effect and the intraday trading volume are also presented.
-
A Stochastic Representation for Nonlocal Parabolic PDEs with
Applications (with
and
).
Mathematics of Operations Research, 47(3):1707-1730, 2022
[Abstract|SSRN|Article]
We establish a stochastic representation for a class of nonlocal
parabolic terminal-boundary value problems, whose terminal and
boundary conditions depend on the solution in the interior domain; in
particular, the solution is represented as the expectation of
functionals of a diffusion process with random jumps from boundaries.
We discuss three applications of the representation, the first one on
the pricing of dual-purpose funds, the second one on the connection to
regenerative processes, and the third one on modeling the entropy on a
one-dimensional non-rigid body.
-
Inventory Management for High-Frequency Trading with Imperfect
Competition (with
,
,
and ).
SIAM Journal on Financial Mathematics, 11(1):1-26, 2020.
[Abstract|SSRN|arXiv|Article]
We study Nash equilibria for inventory-averse high-frequency traders
(HFTs), who trade to exploit information about future price changes.
For discrete trading rounds, the HFTs' optimal trading strategies and
their equilibrium price impact are described by a system of nonlinear
equations; explicit solutions obtain around the continuous-time limit.
Unlike in the risk-neutral case, the optimal inventories become
mean-reverting and vanish as the number of trading rounds becomes
large. In contrast, the HFTs' risk-adjusted profits and the
equilibrium price impact converge to their risk-neutral counterparts.
Compared to a social-planner solution for cooperative HFTs, Nash
competition leads to excess trading, so that marginal transaction
taxes in fact decrease market liquidity.
-
Optimal Tax-timing with Asymmetric Long-term/short-term Capital Gains
Tax (with ,
, and
).
The Review of Financial Studies, 28.9:2687-2721, 2015.
[Abstract|SSRN|Article]
We develop an optimal tax-timing model that takes into account
asymmetric long-term and short-term tax rates for positive capital
gains and limited tax deductibility of capital losses. In contrast to
the existing literature, this model can help explain why many
investors not only defer short-term capital losses to long term but
also defer large long-term capital gains and losses. Because the
benefit of tax deductibility of capital losses increases with the
short-term tax rates, effective tax rates can decrease as short-term
capital gains tax rates increase.
