Research
Stochastic Control and its applications in Mathematical Finance and Financial Economics
Working paper
Monitoring and pay for long-run performance, with Kerry Back, Clint Hamilton, and Ali Kakhbod, [SSRN]
We develop a dynamic principal-agent model in which conditioning future pay- for-performance on monitoring signals is a perfect substitute for contemporaneous pay-for-performance in providing incentives. Average pay-for-performance is higher when monitoring is less efficient, because the conditioning is a less effective substitute in that case. Monitoring efficiency has a greater effect on pay-for-performance when negative signals have accumulated. Using changes in the availability of direct fights for board directors to a firm's headquarters as an exogenous shock to monitoring, we present new empirical evidence on the monitoring-compensation linkage that supports the model’s predictions.
Optimal dynamic contracts and pollution, with Jérôme Detemple, [SSRN]
We examine optimal dynamic contracts when the firm's production generates harmful pollution undermining its productivity. The optimal contract rewards for financial performance and penalizes pollution. The combination of both contract sensitivities incentivizes the agent's effort and environmental (pollution abating) investment. In an economy with a continuum of polluting firms, contracting on firm pollution improves the welfare of the principal and the agent. Calibrating the model to the U.S. economy, we show that the aggregated pollution is reduced by 38.4% if all firms contract on their own pollution.
Process intangibles and agency conflicts, with Hui Chen, Ali Kakhbod, and Maziar Kazemi, [SSRN]
We reveal and study a new empirical fact: Executive and skilled labor pay is increasing in firm process intensity (the fraction of intangibles used to improve the efficiency of the firm). We rationalize this fact in a dynamic principal-agent model. The optimal contract reveals a direct and indirect effect of process intensity on compensation. We verify these effects in the data. In our baseline specification, a one standard deviation increase in process intensity is associated with an 8% increase in executive pay and a 3% increase in skilled labor wages relative to industry peers.
Model ambiguity vs. model misspecification in dynamic portfolio choice and asset pricing, with Anne Balter and Pascal Maenhout, [SSRN]
We study aversion to model ambiguity and misspecification in dynamic portfolio choice. Investors with relative risk aversion gamma > 1 fear return persistence, while risk-tolerant investors (0 < gamma < 1) fear return mean reversion, to confront model misspecification concerns when facing a model with IID returns. Our model can explain evidence for the experience hypothesis, for nonparticipation in equity markets, as well as for extrapolative return expectations.
Robust rationally inattentive discrete choice, with Lars Hansen and Jianjun Miao, [Preliminary Version]
Why is cash U-shaped in firm size, with Ali Kakhbod, Max Reppen, and Tarik Umar, [SSRN]
Best paper in Corporate Finance, Southwestern Finance Association Annual Meeting 2023
We document a new empirical fact: the level of cash holdings is U-shaped in firm size. To rationalize this finding, we develop a model of firm dynamics with costly financing that is not homothetic in firm size.
Heterogeneous learning in product markets, with Ali Kakhbod and Giacomo Lanzani, [SSRN]
Heterogeneous learning abilities among consumers introduce inefficiency to competitive online product markets. Inefficiency emerges due to a learning externality generated by consumers with inferior learning ability.
Robustness and Dynamic Sentiment, with Pascal J. Maenhout and Andrea Vedolin, [SSRN]
Dynamic sentiment arise endogenously due to agents’ attitude toward alternative models. Distorted beliefs generate countercyclical risk aversion, procyclical portfolio weights, countercyclical equilibrium asset returns, and excess volatility.
Forthcoming
Dynamic discrete choice under rational inattention, with Jianjun Miao [PDF]
to appear in Economic Theory
We adopt the posterior-based approach to study dynamic discrete choice problems under rational inattention. We provide necessary and sufficient conditions to characterize the solution for general uniformly posterior-separable cost functions.
The following package provides an efficient algorithm to solve multiple states and long horizon dynamic discrete choice problem [Package]
The dark side of circuit breakers, with Hui Chen, Anton Petukhov, and Jiang Wang [SSRN]
to appear in Journal of Finance
We develop an intertemporal equilibrium model to examine how circuit breakers impact the behavior of prices, trading, and welfare. We show that as the price approaches the circuit breaker, its volatility rises drastically, accelerating the chance of triggering the circuit breaker – the so-called “magnet effect”. In addition, returns exhibit increasing negative skewness and positive drift, while trading activity spikes up. Our empirical analysis confirms these predictions. Moreover, we show that a circuit breaker can affect the overall welfare either negatively or positively, depending on the relative significance of investors’ trading motives for risk sharing vs. irrational speculation.
Performance evaluation, managerial hedging, and contract termination, with Yu Huang and Nengjiu Ju, [SSRN]
to appear in Management Science
Principal of a firm manages the firm termination risk by loading the contract with a positive market component which alleviates termination risk in normal market conditions, but makes termination more likely after negative shocks.
Radner equilibrium and systems of quadratic BSDEs with discontinuous generators, with Luis Escauriaza and Daniel C. Schwarz, [Arxiv]
Annals of Applied Probability, 32(5): 3492-3536, 2022
We present a backward uniqueness result to study the nodal set of Z for a system of BSDEs. Using this result, we prove the existence of an incomplete Radner equilibrium with nondegenerate endogenous volatility in a continuous-time stochastic model of an endowment economy.
Publications
Incomplete stochastic equilibria with exponential utilities: close to Pareto optimality, with Constantinos Kardaras, and Gordan Žitković,
Stochastic Analysis, Filtering, and Stochastic Optimization: A Commemorative Volume to Honor Mark H. A. Davis's Contributions, 267-292, 2022, [Publisher version]
Capital allocation under Fundamental Review of Trading Book, with Luting Li,
Risk Magazine, cutting edge session, 2019, [Journal] [Extended version] [Presentation]
Equilibrium asset pricing under optimal contracts, with Jakša Cvitanić,
Journal of Economic Theory, 173:142-180, 2018. [SSRN]
A class of globally solvable Markovian quadratic BSDE systems and applications, with Gordan Žitković,
Annals of Probability, 46(1):491-550, 2018. [Arxiv] [Presentation]
Convex duality for Epstein-Zin stochastic differential utility, with Anis Matoussi,
Mathematical Finance, 28: 991-1019, 2018. [SSRN]
BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data, with Andrea Cosso and Huyên Pham,
Annales de l'Institut Henri Poincaré (B), 53(4):1528-1547, 2017. [Arxiv]
Consumption investment optimization with Epstein-Zin Utility in incomplete markets,
Finance and Stochastics, 21(1):227-262, 2017. [SSRN]
Long term optimal investment in matrix valued factor models, with Scott Robertson,
SIAM Journal on Financial Mathematics, 8:400-434, 2017. [Arxiv]
Stability of the exponential utility maximization problem with respect to preferences,
Mathematical Finance, 27:38-67,2017. [Arxiv]
Robust portfolios and weak incentives in long-run investments, with Paolo Guasoni and Johannes Muhle-Karbe,
Mathematical Finance, 27:3-37, 2017. [SSRN]
Asymptotic Glosten Milgrom equilibrium, with Cheng Li,
SIAM Journal on Financial Mathematics, 6(1):242-280, 2015. [Arxiv]
Large time behavior of solutions to semi-linear equations with quadratic growth in the gradient, with Scott Robertson,
SIAM Journal on Control and Optimization, 53(1):185-212, 2015. [Arxiv]
Abstract, classic, and explicit turnpikes, with Paolo Guasoni, Constantinos Kardaras, and Scott Robertson,
Finance and Stochastics, 18(1):75-114, 2014. [Arxiv]
Point process bridges and weak convergence of insider trading models, with Umut Çetin,
Electronic Journal of Probability, 18:26, 2013. [Arxiv]
Long-term and blow-up behaviors of exponential moments in multi-dimensional affine diffusions, with Rudra Jena and Kyoung-Kuk Kim,
Stochastic Processes and their Applications, 122(8):2961-2993, 2012. [Arxiv]
Regularity of the optimal stopping problem for jump diffusions, with Erhan Bayraktar,
SIAM Journal on Control and Optimization, 50(3):1337-1357, 2012. [Arxiv]
On backward stochastic differential equations and strict local martingales,
Stochastic Processes and their Applications, 122:2265-2291, 2012. [Arxiv]
Valuation equations for stochastic volatility models, with Erhan Bayraktar and Constantinos Kardaras,
SIAM Journal on Financial Mathematics, 3:351-373, 2012. [Arxiv]
Strict local martingale deflators and pricing American Call-type options, with Erhan Bayraktar and Constantinos Kardaras,
Finance and Stochastics, 16:275-291, 2012. [Arxiv]
Pricing Asian options for jump diffusions, with Erhan Bayraktar,
Mathematical Finance, 21(1):117-143, 2011. [Arxiv]
On the uniqueness of classical solutions of Cauchy problems, with Erhan Bayraktar,
Proceedings of the American Mathematical Society, 138(6): 2061-2064, 2010. [Arxiv]
Analysis of the optimal exercise boundary of American options for jump diffusions, with Erhan Bayraktar,
SIAM Journal on Mathematical Analysis, 41(2): 825-860, 2009. [Arxiv]
Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions, with Erhan Bayraktar,
Mathematical Methods of Operations Research, 70(3): 505-525, 2009. [Arxiv]
Pricing American options for jump diffusions with iterated SOR, with Erhan Bayraktar,
Proceeding of the Fourth IASTED International Conference on Financial Engineering and Applications, 2007.