Abstract : Optimal control is widely applied to understand strategic behavior of agents in financial economics. For example, an investor or a household makes investment and consumption decisions, a firm decides production, investment, and financing policies. Optimal control helps to understand these problems in a random environment facing constraints, risk, and uncertainties. Meanwhile, financial applications motivate new forms of control problems. This mini-symposium presents the latest developments in the applications of optimal control in financial economics.
Organizer(s) : Scott Robertson, Hao Xing
Sponsor : This session is sponsored by the SIAM Activity Group on Financial Mathematics and Engineering.
Abstract : We develop an endogenous growth model with heterogeneous firms facing financial frictions, in which misallocation emerges explicitly as a crucial state variable. In equilibrium, misallocation endogenously generates long-run uncertainty about economic growth by distorting innovation decisions, leading to significant welfare losses and risk premia in capital markets. Macroeconomic shocks that affect misallocation are likely to have overly persistent effects on aggregate growth. Using an empirical misallocation measure motivated by the model, we find evidence showing that misallocation captures low-frequency variations in both aggregate growth and stock returns. Empirically, a two-factor model with market and misallocation factors prices size, book-to-market, momentum, and bond portfolios with an $R$-squared and a mean absolute pricing error close to the Fama-French three-factor model.
[03797] An optimal consumption and investment problem for general factor models : Epstein-Zin recursive utility case.
Format : Talk at Waseda University
Author(s) :
Hiroaki Hata (Hitotsubashi University)
Abstract : We consider an optimal consumption and investment problem with Epstein-Zin recursive utility on the finite time horizon. The returns and volatilities of the assets depend on nonlinearly on the factor processes modeled as diffusion process. The problem becomes a standard control problem. We derive the Hamilton-Jacobi-Bellman (HJB) equation and study its solutions. Under some conditions we construct a suitable pair of sub- and super-solution. And, we prove the existence and uniqueness of solution for this HJB equation.
Finally, we show the verification theorem.
[05413] Patience is a virture: optimal investment in the presence of limit order book
Format : Talk at Waseda University
Author(s) :
Nan Chen (The Chinese University of Hong Kong)
Qiheng Ding (The Chinese University of Hong Kong)
Chen Yang (The Chinese University of Hong Kong)
Abstract : We study an optimal investment problem of a CARA investor trading in a market operated with a limit order book (LOB). The model synergizes three key features of market microstructure: the bid-ask spread, the market depth, and a finite market resilience. Under a Bachelier process for the dynamic of the fundamental value of the asset, we manage to develop explicit characterization through a system of variational inequalities on the investor’s optimal trading strategy. A patience index is derived to highlight the importance of trading timing in reconciling several competing goals such as achieving the current optimal risk exposure, incorporating the trading signals about the future, and minimizing trading impact costs.
[05411] Why is Cash U-Shape in Firm Size?
Format : Talk at Waseda University
Author(s) :
Hao Xing (Boston University)
Ali Kakhbod (UC Berkeley)
Anders Max Reppen (Boston University Questrom School of Business)
Tarik Umar (Rice University)
Abstract : Cash holdings are U-shaped in firm size. To rationalize this finding, we develop a model of firm dynamics with costly financing allowing for heterogeneous size} Cash is U-shaped in firm size because of decreasing returns to scale and hedging incentives. When a firm is small, cash decreases with size because investment opportunities are better resulting in more aggressive investing. Investing slows as the firm grows, and eventually, cash increases with firm size to hedge larger-scale cash flow shocks. Our model likewise explains why in the data issuance amounts (payout rates) are U-shaped (hump-shaped) in firm size.
Abstract : This paper studies how a borrower issues long- and short-term debt in response to shocks to the enterprise value. Our theory highlights the tradeoff between commitment and hedging. Short-term debt protects creditors from future dilution and forces the borrower to reduce leverage after negative shocks. Long-term debt postpones default and allows the borrower time to recover after a downturn, thereby providing hedging in the upturn.
[05611] Nonlinear Dependence and Households’ Portfolio Decisions over the Life Cycle
Format : Online Talk on Zoom
Author(s) :
Wei Jiang (HKUST)
Shize Li (HKUST)
Jialu Shen (University of Missouri)
Abstract : This paper uncovers the nonlinear relationship between earning risk and stock returns, as measured by the between-squares correlation. By incorporating this between-squares correlation into a life-cycle model, we demonstrate that it lowers households’ participation rate and generates moderate risky asset holdings. We identify two pathways through which the between-squares correlation affects portfolio choices: the skewness and kurtosis channels. The extent to which these channels dominate each other depends on the level of between-squares correlation, leading to a nonlinear relationship between this variable and household decisions. Our empirical studies support the model’s predictions. Moreover, we find that ignoring between-squares correlations leads to substantial welfare loss and contributes to increasing wealth inequality.
[04014] Dynamic Equilibrium with Insider Information and General Uninformed Agent Utility
Format : Online Talk on Zoom
Author(s) :
Scott Robertson (Boston University)
Jerome Detemple (Boston University)
Abstract : In this talk, we establish the existence of equilibrium in the presence of both asymmetric information and general preferences for the uninformed agent. Specifically, there is an insider who possesses a private signal about the terminal value of the traded asset, and an uninformed agent who possesses no private signal. While the insider has CARA (exponential) preferences, the uninformed agent’s preferences are described by a general utility function defined for positive wealth. The terminal value of the traded asset is a function of a time homogeneous diffusion. In this setting, and under mild conditions on the diffusion, terminal payoff function, and uninformed preferences, we establish existence of a partially revealing equilibrium, where a market signal is communicated to all agents at time zero. Additionally, the equilibrium is a rational expectations equilibrium in the univariate case. As the uninformed agent preferences are general, we are able to obtain sensitivity of the asset price, volatility, and market price of risk, to the uninformed agent’s initial endowment, as we will show through examples. This is joint work with Jerome Detemple of Boston University.
[05665] Strategic Investment under Uncertainty with First- and Second-mover Advantages
Format : Talk at Waseda University
Author(s) :
Zhaoli Jiang (The Hong Kong Polytechnic University)
Min Dai (The Hong Kong Polytechnic University)
Neng Wang (Columbia University)
Abstract : We analyze firm entry in a duopoly real-option game. The interaction between first- and second-mover advantages gives rise to five regions in the unique Markov subgame- perfect symmetric equilibrium featuring state-contingent pure and mixed strategies. Second-mover advantage induces firms to enter probabilistically when market demand is high or medium. Follower enters immediately after Leader does in the former scenario, but waits until demand further rises, allowing Leader to earn monopoly rents in the latter scenario. When demand is low or medium high, firms wait with probability one. Finally, when demand is medium low, firms rush to enter as first-mover advantage dominates.
